I'm working on changing the character battle graphics right now, and as far as I can tell, they all work fine for other characters. I haven't done extensive testing with damage and such, but I think they all work fine. The auto-commands (Cover and Hide) are tied to a particular character, though, so if you remove these Cecil and Edward will still perform the auto-action. Likewise, if you add them to another character that character won't perform the auto-action. Anyone know where this information is located?
There are two graphics used for special moves: the 16x24 casting graphic and a special 24x24 graphic. For magic users, the casting graphics are always used for magic. Other commands that use casting graphics only use the first one, not the second part of the animation (usually open mouths or glowing things).

The other graphics are tied to particular commands like so:
Dark Knight Cecil (Special: Dark Wave, Casting: guards his face with his blade)
Kain (Special: Jump)
Young Rydia (Special: Call)
Tellah (Special: Recall)
Edward (Special: Hide, Casting: Sing)
Rosa (Special: Aim, Casting: Pray)
Yang (Special: Kick, Casting: Store)
Palom (Special: Cry)
Porom (Special: Focus)
Paladin Cecil (Special: Cover)
Cid (Special: Peep [lens far], Casting: Peep [lens close])
Older Rydia (Special: Call)
Edge (Special: Throw)
FuSoYa (Special: Regen)
Let me know if I missed one (I think the other actions I didn't mention just use the victory arm raise or other basic graphics). The special graphic is always used for special actions, so if you give Yang Jump for example, he'll use his Kick graphic for the Jump action.
Edit: I have the offset locations of each character graphic if anyone wants them.