See below the table for notes on character names.
Story character names and the first few gacha character names are taken directly from the game files, but after that point Square gave up and started naming everybody "Character_29" and the like. I've used canon transliterations for characters that exist in Valkyrie Profile or collaborations. I've also done research on name meanings to clarify some transliterations, but I have phonetically transliterated Hakurei, who has several translations for the kanji in her name.
Edit (11/14/2018)- I added all the existing limited skills and 3 characters left to add. All the mistakes you notice, feel free to change. I do not know how to fix the table bug that the icon images do not appear but when you edit they appear.