weapon animations and constant spell effects

Characters after Umaro (Umaro, Banon, Leo, The Ghosts, Biggs and Wedge) are all characters that cannot be unequipped, so you can just give them a regen ring and that'll work.

I don't think there's any piece of equipment that, once equipped, will not be removeable (like the Deadly Sword/Armor in Lufia 2)... So, other than going to the actual game and creating a new relic that is unequippable, I don't know