The reason you can't cure Stone in battle is due to this game's roots in D&D. Softening a stoned character takes hours. Not exactly something you can do in one round of combat. Same reason LIFE doesn't work in battle. Resurrecting takes a long time.
As for the menu, it's hard to picture how Left/Right would work, but if the others are Up/Down, I think it makes more sense for it to be Up/Down.