Is there a list of all the possible mutations that can be gotten? also do they change how the MC looks or are they mostly just in the mutations status screen?
There are major and minor mutations. Minor mutations are just stat boosts and all major mutations are visible. You get (I think) three minor mutations and one major mutation every time your integrity gets too low. Major mutations are:
Tail, eyes, back spines, face scales, body scales,horns,wings.
