As to your cock bird losing his tail feathers, it is the season. Several of my birds look like they had an unfortunate run in with a weed eater, just natural molting.
Occasionally when a broody has a batch of mixed age eggs and only a single chick hatches, the hen will stay on the nest figuring the rest should be hatching now as well. If the chick stays with the hen it should be ok, but sometimes a rambunctious chick will get away from the hen, resulting in getting chilled and dying, and or eaten by maybe rodents in coop, or the other chickens. Better results will almost always be achieved by having all eggs at the same stage of incubation. I know it seems heartless to discard eggs that are already started and replace them with fresh, but you'll likely end up with more chicks with the later.
Unfortunately both egg eating, and to a lessor extent tail picking, can be a learned behavior that can spread through a flock. Spend some time, and keep a close eye on your birds. If one of your birds shows regular sign of yoke on her, or is seen picking at other birds enough to cause problems, your flock would be healthier and happier without them.
