Our chicken will not get out of the nesting box/coop for over a week and now she is beginning to lose feathers around her face. This is the only one with this issue. Please help! You have a broody hen
You don't have to have a rooster in order for her to want to nest, it's just her nature.
If you don't want her to be broody, search for "broody buster", sometime it will work.
As far as the face feathers missing, check her over to make sure she doesn't have any lice/mites. Sometimes broodies don't take enough time out to dust bath and preen, so mites/lice can become a problem.
She is beautiful and I must say I do love the second photo of her where she looks like a porcupine.