If i had a guess I would say Defiantly Broody. Especially with the large poo which they tend to do because when on eggs they can't go as often, so they do it in a large mass all at once. And with the feathers on the breast gone, then that says it for itself that yes she is. I personally wouldn't right now let her hatch eggs. It will be very cold and the chicks won't hatch for 21+ days. By then it'll be quite cold. The hen should spend the winter resting and taking time off not constantly worrying and fussing over baby chicks. Thats what Spring and summer is for. Hope this helps!