I don't know of anything specific that would cause this.
But considering how the wing and the foot are affected, yes I would guess the chick might have something going on genetically.
I don't know the answer about laying, but I would be concerned about picking by flockmates or about her not having enough feathers to protect her from the weather.
As a practical matter, if she seems to have trouble at any point, I would consider euthanizing her or processing her to eat. (I don't think this would make the meat unsafe to eat, but if you see her as a pet you might not want to eat her.) But if she continues to be active and seems to move easily and eat well, I would keep her as long as she stays healthy and you want to keep her.
If she ever does lay eggs, I would not try to hatch chicks from her, in case the condition would be passed on to her chicks. But if she were to go broody, she could be allowed to hatch eggs that were laid by other hens. I don't see anything that look contagious here.