SC:Lost Swords Synthesis Translation/Guide and FAQ

You increase the abilities of items in this game by synthesizing them with the different types of crystals you get during the game.  By going to the character menu and the synthesis (合成） option you can pick an item using X and use (SQUARE) to select the gems you want to synthesize with the item to increase its attributes.

 From what I can tell all the gems cost the same amount of gold to synthesize but "rarer" gems (indicated by the letters in the bottom left circle in their thumbnail) give more EXP for levelling up an item.  The ranks I've seen so far are N, HN, and R (R being the rarest and N being the lowest)

The Rarity of items limits how "good" an item can get from synthesis, you won't see a N weapon jumping from 50 to 200 attack after a few levels.  It's a good idea to save your good gems for when you get lucky on a nice Rare weapon or armor and then just pump it full of stuff getting much more out of your gems. There are some later levels in the main questline where if you don't have enough damage breaking their element armor in the time limit is next to impossible without a properly upgraded weapon.

FAQ:
How should I spend my gold to upgrade my weapon?
I recommend you save it to upgrade a rare weapon with a rare or higher gem.
Synthesizing with gems always costs the same amount of gold no matter the rarity, so the most important thing is the EXP that each rarity gives which, as far as I've tested, is a flat rate depending on its rarity
N gems: 1125 EXP
HN Gems: 3000 EXP
R Gems: 5000 EXP
Finally you will want to consider the prefixes on the gem if you have multiple rares.  Choose which one suits what you need/want the best using the list later on in this FAQ.

Does the Element of the Equipment effect it's stats/abilites?
Yes! BUT ONLY for higher rarity equipment, you can tell if your gear has extra damage/resistance to elements if it has two little green tabs you can scroll through with L1/R1. So early on the game the normal gear you get will just be different colors, but once you get into the HN, R or greater rarity equipment look for that extra tab.  Almost always the color of the gear corresponds with the bonus it gets.

How do I get FP to buy things in the shop?
You get 10FP by completing quests with someone you have shared friend codes with as your support character.
(This only seems to happen ONCE per friend you add)

How do I get friends? (hah)
Well you can either share your friend code with someone and hope they accept or accept other peoples requests from you in the "Battle Comrades" section under the 戦友 menu. You can find your friend code under the second option in this menu, and while looking at your friend code is you press (X) you can add someone elses (if they've given it to you)
Lastly back at the main 戦友 menu the 3rd option shows if you have any pending friend quests.  If you want FP don't worry about what level they are just take them along for some random low level mission and voila free FP!

Item Description (Right side of the screen, left-most green tab)
攻撃力 - Attack Power: Damage
ウィポンアーツ - Weapon Arts: Determines what A+B super you have
特性 - Special Attribute:  Some weapons have special abilities
      ガード崩れ - Guard Crush: moves chip away at guard gauge faster.
     無敵切り返し it says invincible Muteki Kirikaeshi, but I'm not certain what Kirikaeshi is referring
      too in game terms.
     There are a bunch of others I haven't seen yet I'll try and post the new ones when and if I get
      them.
合成ランク - Synthesis Rank (I'm not sure what this does in relation to synthesis but bigger is better here?)
追加スキルスロット - Additional Skill Slots: Slots For Skills
売却価格： - Sell Value
男女兼用装備： Both Genders can wear. 　（男：Man女：Woman there are some gender specific clothes)
<Character name>が装備中: Is currently equipped on (Character Name) There also is a little E on the item icon that tells you too.


Gems:
All of the gems (that I've seen) are written with this template Prefix -(of)- Gem Name
IE: 攻撃のミルキークォーツ  Attack - of - Milky Quartz (or Milky Quartz of Attack so it doesnt sound like engrish)

The prefix determines the properties the crystal will give you, and if it has the attack or resistance property the element type it gives is determined by the color of the crystal.
Red - Fire, Blue - Water etc etc.
Prefix Translation:
攻撃 - Attack:  Boosts Element Damage you Deal
横攻撃 - Horizontal Attack: Boosts Damage of [A](Horizontal) Moves +#%
紙一重 - Paper Thin: Boost Damage of Counter Hit Attacks +#%
耐性 - Resistance: Reduces Elemental Damage Received+#%
カウンター - Counter: non-CH attacks have a chance to randomly be a CH.
自動弾き - Auto Repel: Random chance to auto Guard Impact (when blocking only, I have tested this tis silly fun)
友に捧ぐ - Supporting Comrades: Increases the damage of your support character +#%
連劇補助 - Repeated Attacks Booster: Reduces pushback of your attacks on hit
敵弾き - Attack/Foe Repelling: Increases pushback of your attacks on hit  +#%  (these have  強襲(assault) in their description so I assume it only applies to when you're attacking ?)
間合い変えず- Decreasing/Amending Distance:  Decreases pushback on block -#%
間合い開き- Increasing Distance:  Increases pushback on block +#%
 (I believe both of the block distance gems effect both you and your opponent since it says  常時(ordinarily) in the description of the skill)