There's a twist! When a character goes back to their world, they don't ACTUALLY go back. Everyone is a copy of the original (who is happily living in canon-land!), so when they "go back", what actually happens is that they're simply erased from Kiseki itself. Charas who return are created again, and they're given new memories of their canons. That's how the whole "I went back and then two more volumes of my manga happened!!1" thing works.

So, yes, any permanent change made on Kiseki would be re-created for the sake of sticking to that character's in-game!canon.

Very, very minor cuts get healed just a tiny bit faster than usual. And yes, it is possible to get scars! Healing doesn't mean "perfect" healing. If you got an arm chopped off, for example, it wouldn't regenerate (like, Celes!Kurogane's didn't).