Problem with manufacturer claims is they're often using bare legal minimums (like commercial farm numbers) to calculate space. Not surprisingly chickens in factory farm settings have their beaks cut off to prevent them from killing one another due to stress and crowding.
Recommended minimum space on here is 4 sq ft in coop, 10 sq ft in run, but as those are minimums if you can exceed that, it can only help.
Very normal with the nest boxes. Even if you had 20 boxes they'd likely pick one or 2 favorites.
Lots of nibbling, probably starting with feet and working up. Very unlikely for rats to kill adult chickens, however rat burrows can serve to allow other predators like snakes and weasels in. If you saw no obvious chew marks it wouldn't be a rat.
So these are obviously bigger runs that yours, but there's a lot of examples and suggestions on here to think about:
https://www.backyardchickens.com/threads/a-cluttered-run.1323792/
Yeah if you enjoy that chicken I think a separate enclosure for the times you can't free range would be best and safest, especially since you can't free range all day to help alleviate any crowding stress. The coop you have right now would certainly be big enough for her alone.