Well I had a chick who lost her toenail (she had a huge lump of dirt on the end of her toe that stopped circulation). She still doesn't have it back after 10 weeks and I'm not sure if she ever will, but now it's her special thing
Yes, that's frostbite. The toe/foot will eventually fall off. Keep her inside the house or in your garage for a bit.
What do you mean by "she lives outside"? Does she have a coop and a flock?