I like the poor crystallizing girl concept as well. Maybe she could be the wizard who has foregone gender roles because of her state. The cat wings or no could simply be someone who likes to hang around, her lonesome friend.
My idea with your genderless wizard/witch is maybe they are a Jykell and Hyde like character where they are both genders but can't figure out which one they truly are. Prehaps the male side is trying to over take the female side of things and the female side has to fight to keep herself known. This could be a result of character going somewhat insane do to the two personalities. The winged cat could simply be a concious to either the genderless character to help them with their personality disorder, or to the crystalized girl who seems to struggle through the fear of being shattered, so she closets herself. But prehaps the crystalized girl must over come her fear from being shattered and leave her isolation in order to free herself from being glass and she must find this wizard to help her become human?