My Opinions as they relate to Pirates and a general view of the TK
While it's certainly the case that I speak about it based on my experiences with Mel, it also only makes sense that I should have an opinion because of it. Of course I'm biased more than a non-TK, but at the same time I've researched it more as well. TK provides the least benefit for Mel past the capability, and this IS primarily a build issue. However, I believe the deeper problem stems from the fact that TK isn't a particularly succinct class, especially out of all of the psychics. It's somewhere between a psychic combat warrior and full on support. I also believe it has the problem of a rather rigid build in general as opposed to some of the other supernaturals like elementalists, medium, or ninja. In addition I find the AP costs of some of the feats to be disparate with their relative worth. The Bound features are rather weak for their cost, whereas TK Burst is incredibly strong for its cost. The base Telekinetic capability is an AMAZING one, but the features offer little consistency between whether the class is supposed to be support or a psychic warrior. As far as Melanie having the class goes, I have no issue with her BEING Telekinetic, it's just that after seeing a lot of the 1.04 supernatural classes and their relative power, it's quite clear that TK is balanced entirely around its capability and capstone instead of offering interesting variety or gradual power growth as Ninja, Medium, or the Elementalists do. Of course I benefit by not going deeper in TK compared to say Telepath since I don't need to spend AP to activate it, compared to Telepath.

Suggestions
As far as suggested changes, I'd say PK Combat should get rolled into the base class feature and give THAT either an activation or Bind cost, make PK Finesse passive OR retain the bind but with a better benefit for a TK build as opposed to a Medic/item user build, and add a new feature to replace PK Combat. IF PK Combat remains separate, it may also be of use to offer a bonus of some sort in the event that the trainer has Master Combat, as PK Combat is useless but required for PK Finesse in that case. While Kinesis certainly has a use, the way the Moves are arranged is a little awkward. One move in PK Alpha is strong early game and the other weak, and then they switch in relative advantage late game. They're also both non-damaging attacks for a class with offensive stat tags, and between the elemental connection, Focus ranks, and any other edges for other purposes, it can be hard to fit Confusion in for some time. It would help class coherence if there was a larger pool of moves to pick from, which is true for all of the psychic classes. It could still be two ranks of two moves, but opening up more psychic moves, such as Psybeam and others that don't quite fit into any specific category, could help better define what the class is supposed to be. Telekinetic Burst actually seems on the cheapside for what it offers. It may also serve to actually increase its cost or change it to Scene xN and absorb some of the costs of the other features.


PK Combat
PK Combat permanently puts the user down 1 AP while it's up and functionally only lets one act at the efficacy of a combat-oriented attacker. 1 AP in more mundane classes gets you things like a variety of small but effective boosts as per Cheerleader, customized buffs as per Dancer, bonus Struggle attacks as per Hunter, immediate switches with Juggler, every Martial Achievement, and generally benefits that are fairly unique over base edge/combat mechanic use. I would argue that while spending one feat over 4 edges for effective combat maneuvers can be good, the feature point is generally worth more, and there's no way to reach the capstone without this feature. For some builds, this feature is just a waste if they planned on raising combat, or had to for prereqs somewhere else.

PK Finesse Item Use
The ranged use of items from PK Finesse can certainly open up opportunities, but many of the ally support ones are a waste to use without Medic Training, and though it may be a rather accessible edge, it's more the case that it's a less common build than that Mel's doesn't use it, especially given that without it a forfeited standard action likely generally results in a bigger loss than the gain MOST restoratives would offer. The Full Heal, Hyper Potion, and Revive are amonst the most useful common-use items, and they have uncommon enough effects that a trainer performing them is likely the best use with regards to opportunity cost. However, the advantage of using them at range varies. The value of health restored must first be high enough proportionally to the ally's max, but would likely be the best use, as a trainer can stay far behind an ally built for tanking. Full Heals are similarly useful as it can reverse attempts to disable an important ally, but stacking statuses on one target when multiple exist is not generally good strategy, especially given that some statuses can be cleared or handled in other ways. Revive functionally would not be of much use, as an ally being revived in the middle of combat is incredibly vulnerable and it would be unusual for fighting to have drifted that far from a fainted ally for the added range to be of much benefit.

PK Finesse Weapon Use
Regarding the weapon-use portion of this feature, it doesn't offer much Confusion can't without a MORE specific build as opposed to a general one, and the general build makes more sense to be accounted for. While the attack is physical instead of special, struggle attacks generally aren't strong enough for that to be meangful outside of desperation or a curious and irregular encounter where EVERY enemy has high special defense.

TK Burst and AP Costs
The costs imposed on these two features seems out of sorts with Telekinetic Burst, which is considerably more powerful (granted PK Combat would aid its use in the standard and expected TK build). Effectively, it's quite expensive in terms of opportunity cost to use PK Combat and PK Finesse without Telekinetic Burst, which is more in line with the benefits of a 2 AP skill that effectively costs 2 AP  for its first use and 1 each time thereafter. Of course, the standard TK build very likely will take it and has no reason not to at that point. The damn thing is inordinately strong for 1 AP and could probably serve to have its cost increased or changed to Scene xN.

TK Moves
I understand move pools are much more limited for the psychics than elementalists by necessity and I keep that in mind when comparing. As far as other moves that by their vidya descriptions could also fall under TK, I could only really come up with Gravity, Magic Coat, and potentially Mirror Coat. I know Warper gets two of these, but one is literally described as a barrier and is a bit redundant for Warper for having access to Magic Bounce as well, and the other is a downward-directed force which is fairly easy to imagine for telekinesis.
-Telekinesis is certainly useful in virtually every fight.
-Psychic is also likely to at least be reliable, though it seems at odds with the heavy offensive/defensive support structure for the rest of the class. I understand it was quite obviously telekinetic in the source material and as the apex Psychic move it makes sense to include it here.
-Kinesis DOES have the possibility of saving a fight, but it is mathematically unlikely to be available when you most want it. With regards to type advantage (the most reliable way to have a deadly attack) or a finishing blow, suppose the attack is AC2. We'll give the defender 6 evasion from status without any further muddiness from abilities or some such, raising the effective AC to 8. Kinesis will only make a difference on a roll of 8, 9, 10, or 11. Since we can ignore a roll of 1-7, there are 13 potential hit rolls and only 4 for which Kinesis matters, giving about a 31% chance of activation. Now for AoEs, let's look at say AC4, a common enough standard for explosive ranged blasts. In the same situation, Kinesis only has a 36% shot at making a difference. To even make it to a coin flip, you need an effective AC of 13. Of course, as an Interrupt the move is ONLY spent when it will actually prevent an attack from landing and as evasion rises and accuracy falls it has a steadily increasing chance of being useful, but getting it to a reliable level is difficult and requires a considerably specialized build or circumstances. It's certainly a bonus that Trainers don't have a move limit.
-Barrier has the opposite problem of inversely scaling in efficacy as a campaign progresses. With 20 HP, 15 DR, and psychic typing, it takes a 35 damage hit at once to drop it. This can be hard to reach early game, making it an incredibly powerful move then. But it doesn't take long before this number is effectively guaranteed by even a minimum damage roll of an attack of neutral type effectiveness. While it can certainly limit an AoE attack even in end game, there are several ways to completely bypass it, it isn't an Interrupt, and it costs a standard action. Even simple shifts can often get an attacker completely around the segments. Its most effective uses seem to be to either box off the user or an immobile enemy, but both have drawbacks.

TK Abilities
-Interference seems dangerous compared to the otherwise long-ranged nature of the class, but it can certainly be effective.
-Levitate as per the Ground immunity is somewhat limited in usefulness, as a lot of Ground attacks are limited by being dangerous to allies. Of course immunities are GOOD but this ability's main draw seems to be as a source of the levitate capbility for trainers. But even in that regard, it's hard to actually open up real utility with that as opposed to just fluff flying. If you're outdoors or in the open, it's trivial to have a pokemon act for you. In more confined spaces, acrobatics or simple ingenuity can get the job done. The circumstances by which you have access to none of these things are incredibly rare and obscure. Of course, many abilities are right on level with this and it's certainly fine as an ability, it just doesn't offer quite as much as it may initially seem.

The Telekinetic Capability
The main draw of the class for me personally and I imagine many players. Being capable of doing it without a pokemon is of course incredibly useful. In the average case though, it's no better than Power. Yes it can be done at range, but I believe it's possible to get the Power capability higher than one can get their Focus rank. I could be wrong, but if it is that effectively means it's more of a trade off than an advantage over high power trainers. The cases when you don't have access to your pokemon and the capability straight up allows you to do something you couldn't otherwise do with a little planning or ingenuity like pulling your lightsaber to you after being attacked by a wampa do seem incredibly rare and more tailor made for a telekinetic than naturally occurring. Maybe you can pull the keys to a cell to you, but in a world where psychics aren't that rare, presumably that should have been accounted for so you're relying more on an inept enemy than the capability. I don't believe it's necessarily much better than the rare capabilities granted to elementalists. I'd rate Illusionist, Shade Caller's living shadow, Wind Runner's One With the Winds, Spark Master's Magnetize, and Swarmlord's pheromone manipulation/bug communication to be vary close in terms of non-combat use with Telekinesis.

Other Psychics
Telepaths suffer a similar inflation of AP, requiring 3 AP for the first use of 1 AP features, the first of which only offers real advantage in battles where your allies and enemies are heavily mixed together, which is already problematic with the addition of flanking for grid users, and it isn't all that hard to avoid hitting allies with aoes for abstract distance users. The Inception-esque feat also requires effectively 3 AP for a use, but at the very least CAN hold very strong combat or fluff benefits and it's up to the whim of the GM. Of course it's cheaper if you're holding it up between scenes, but you're already in pretty strange territory at that point as far as what you're doing that it's hard to really comment on. At least TK has its capability entirely passively, it's a little strange that Telepaths could potentially lack the AP to read minds, or that it's a Swift ACtion rather than a Free Action. Furthermore, the capability can be resisted and as it only reaches to surface thoughts isn't guaranteed to reveal new or useful information. The moves Telepath learns are almost entirely dependent on another class, as the only psychic attack it can learn is Confusion. Its Special Attack stat tags (which still differ from its base Class tag of Def and Sp. Def), use of Calm Mind over Amnesia, the combat mechanical benefit of Mind Reader, and many opportunities to use Psych Up provide no actual benefit to the class itself.

Clairvoyant is similarly nearly entirely GM driven compared to the simple mechanics of Warper and TK, but at a much cheaper cost. Of course, scrying isn't done offhand like telekinesis or telepathy, but the Moves it learns put it right in place as the most easily offensive psychic class as well as being definitively useful.

Warper most curiously has no AP costs for the entire class and yet offers heavy advantage via the Teleporter capability. While its features are Daily instead of AP or Scene based, it offers effects that truly are not reproducable otherwise. While one could simply walk instead of teleport, teleporting is instantaneous, so it isn't really analagous to the TK v. Power comparison. It's also quite mechanically powerful for not being nearly as GM-moderated as Telepath or Clairvoyant.

Elementalists
While there's only one per type as opposed to 4 and this gives them the whole breadth of the type to be built on, I don't think the better capabilities among them are any weaker than the psychic capabilities. They benefit from being the sole representative of their Type with regards to move availability. The frequency with which many types can get Immunities to certain things also shouldn't be overlooked in how powerful the class can be concerning fluff. * Denotes those elementalists that I consider to be on par with psychics in terms of non-combat strength.

*-Prism's Illusionist is an incredibly rare capability that Guile doesn't even compare to. I'd definitely rank it on par with psychic capabilities and as a class as a whole considerably superior to all but Warper. Rather than be strictly handled mechanically or performed at the GM's whim, it offers the player near complete control in how it's performed. Combatwise, it gets some of the most reliable and useful normal attacks and while only one feature isn't static, it doubles as both a way to increase your chance of doing damage or also drastically increase your damage dealt.
-Fire Bringer is primarily combat oriented, but is incredibly customizable in that regard. Costwise, it has a solid,reliable 2 AP ability. Can't say much on it.
-Tidedrinker's Gilled capability is of course easily handled by a mundane trainer in a number of ways, and relies heavily on the setting as far as how useful it is. It's certainly on the weaker side of supernatural capabilities, but in those rare circumstances where it shines it's glaring. Bending Current is also incredibly versatile.
-Druid is similar to Tidedrinker in relying heavily on the environment, but with even rarer circumstances for unnaturally strong capabilities. Its cost ability is somewhat limited, but comparable to something like Barrier.
-Stone Warrior is a good example of an AP Binding feature inherently useful to the class instead of relying on atypical builds. Not only does it offer versatility, but even bonuses when a stance is redundant.
-Earth Shaker loses a lot of advantage with abstract maps unfortunately, to the point that its 2 AP cost move is not nearly on par with most others, and even on standard maps, doesn't seem particularly impressive.
-Steelheart is a fairly straightforward class just loaded with effects that are nearly always useful.
*-Shade Caller's access to Darkvision and Mindlock in my opinion also put it on terms with psychic capabilities for non-combat purposes. While flashlights certainly exist, it can be hard to bring sufficient light for some cases and the advantage of being able to see is significant. Furthermore, Mindlock isn't particularly accessible to trainers and would aid out of combat significantly in undermining the power of psychics in the cases where they ARE truly unique. Of course, Dark IS the psychic-killer to begin with. The living shadow is a strong effect to be completely passive, and the cost ability is actively designed to combat the class's weakness. Add on the rare and powerful Ability options and it's on par with the psychics in terms of capability and stronger in combat.
-Miasmic is a simple class like Fire Bringer, but with a rather interesting non-combat effect of not being able to be poisoned. Of course exactly how this applies is incredibly variable, but it's certainly quite rare and nigh impossible to reproduce.
-Frost Touched is functionally similar to Earth Shaker, but the Ice Shield ability is notably similar to Barrier's use. It's weaker, but if Barrier is already easy enough to drop, Ice Shield's use as an interrupt is quite strong.
*-Wind Runner has one of the most interesting abstract capabilities in One With the Winds. Costwise it was placed on par with Telepathy or keeping both TK binds up, but oddly enough it offers no mechanical benefit whatsoever and doesn't have the obvious and powerful uses of those other capabilities/features.
*-Spark Master also has a unique capability in Magnetize. While it's entirely abstract and relies heavily on player knowledge, the ability to manipulate magnetic waves is incredibly powerful with the assumption of modern technology. Of course it's not as easy to apply as the other high-powered capabilities.
*-Swarmlord is another such capability that can be quite abstract in how one perceives it may be used, but considering it's very hard to NOT have bugs somewhere, it's like having an information network everywhere.
-Appariton's Shade Walk actually seems to have too heavy a cost to me. While functionally, the ability to shift through solid matter is incredibly strong unless you aren't even standing on ground, it still has the penalty of health loss when using the actual capability. It's effectively most expensive in combat while also being the hardest to use in that case.
-Herald of Pride's Peerless Sovereign likewise seems needlessly expensive. There is a variety of ways to boost all sorts of rolls, including accuracy and evasion, by a few points for only one AP, so gaining only +1 for an attribute at the cost of binding 2 seems weak.
-Glamour Weaver doesn't quite gain any new capabilities, but it does have an effect that seems to represent a solid 2 AP cost.