LP: rarely used. You can use it as anti air to cross under.  You can also tick throw with it and tick into karakusa.

In combos: LP>LP>LK light Hayate (you can skip one LP)
LP>LP>SA1 (pretty sure this is a thing)

F+LP: Never used but you can also use it as an anti air. Not really a big difference between F+LP and regular LP.

cr.LP: same as regular LP.

j.LP/j.LK: you can see it used as a reset after SA2 combos.

What I forgot for cr.LP is that you can cancel your recovery frames for a dash which makes your movement even faster.  Used if you stun someone but you're far away.

(overview of light kick): You can tick it into karakusa. Kara-cancel it into karakusa. Use it as a reset it in the corner after ex.hayate. And also cancel it into ex.oroshi or lp.hayate

LK: kara into karakusa for more range. That's the common thing to do. You can also cancel it into lp.hayate and ex.oroshi(edited)
F+LK: use it after ex.hayate it in the corner. Works on pretty much everyone iirc. I haven't wrote down a list for it yet so I'm not exactly sure Not really used outside of that
cr.LK: Used to punish high blocking the most especially after hayate loops. Cancel it into lp.hayate. You can also cancel it into ex.oroshi to punish low blocking.
Tominaga likes to spam it if they are on low health

j.LK: you see it sometimes and it's definitely better than j.LP but still isn't very common.(edited)
I forgot to mention that cr.LK is also used to combo into SA1
[6:48 PM] Ryssen: you see people dash in cr.LK>SA1

(Overview of medium punch): The normal you should use to cancel into SA1 since you get a lot of time to do it which makes it perfect as a hit confirm. This should be your most used normal since it converts into everything useful. st.MP is also advantage on block which makes it even better.

MP: Canceled into hayate and SA1. You can also ex.oroshi but with everything else (except HP) it doesn't combo. Because of the blocked advantage you can sneak in a karakusa if you cancel into it late enough or you can dash in after blocked MP and throw them.

Combos: MP>(can also be crouching)LK>lp.Hayate
MP>SA1

Misc: You can combo it into itself if you meaty it.
[6:57 PM] Ryssen: Mimora likes to hayate cancel a blocked MP and do either another MP or cr.LK
F+MP: Used to gain distance. You can link it into SA1.

cr.MP: Really long range which makes it an ideal poking tool. You can also cancel it into SA1 or hayate.

j.MP: not used.

AA s.MP: A really good anti air tool as you can either dash out if they parry it or cancel it into ex.oroshi
MP and cr.LK are used for hayate loops since MP is a high parry and cr.LK is a low parry

(Overview for medium kick): Not used a whole lot for a few reasons.
MK: you can AA with it but why would you.
F+MK: never ever used.

cr.MK: this is the gold of medium gold. It's block advantage so you can harass with it. Mimora likes to link it into SA1 after karakusa because it does the most damage (doesn't scale as much). Outside of karakusa it doesn't beat HP but it still does more damage than MP.
You can also AA with it and dash away if they parry it. Alright AA

j.MK: it's a nice jumping poke and you can cancel it into SA1. You can also combo it into LK/LP if you do it low enough

(Overview for hard punch): the only button you can use to cancel into SA2. Otherwise a risky button since it's pretty slow and you can easily be punished for using it.
HP: canceled into ex.Hayate for corner carry and into all supers.
cr.HP: the sweep, use with caution.
F+HP: Actually not terrible, you can use it to punish dashes if they are far enough away
j.HP:  You can combo it into HP but it's fairly strict timing on it. This is still a good button to use


(Overview hard kick): used in some matchups.
HK: Used again Elena for some reason, not exactly sure why.  I think it punshes her throw box away so that's a thing.
cr. HK: Used again Dudley to beat machine gun blow and as a AA against him. You can use it as a AA.
F+HK: you can hold it to gain some distance but I'm pretty sure canceling dashes with cr.LP is faster just a little tricker to do.
j.HK: The air to air normal you should use. You can cancel it into HP if you do it low enough and it's a fantastic poke.

OU: you can be sneaky and tick it into karakusa. You can also combo it into SA1 if you meaty it.