Do you have any roosters? I don't think the back end is mating damage, but want to rule it out for sure.
I think both areas look like feather picking / over-grooming. Probably happens on the roost at night where you can't see it, if you haven't seen them doing it. Other hens are eating this one's feathers. Under her neck especially - she can't reach those herself.
Solutions are feed more protein (recommend 20%), more space in the coop, more things to hide behind in the run and more space there too, reducing stress in their lives, and if that fails, pinless peepers. It's a bad habit you want them to stop doing asap. If you can identify the culprit(s), remove her from the flock for a few days, and see if she quits. You can put a chicken saddle on the afflicted hen to protect her saddle area, but it won't get better until after she molts.
