It will be back, and she will take a chicken with you standing in the yard only a few feet away if it gets a chance.
I'm thinking your hen was bouncing off the run walls and that's how she got cut up.
I'm in upstate NY also, and Yogi has been very active in my area. This guy is big, and took two bags of garbage off our front porch. Backyard is fenced in so the dogs do a good job of keeping him and other predators out.
I'm in NY also. I'd open both gable ends up. Or at least one if you could get some of those transom Windows open. Don't worry about the window being at roost hight. The gals will love it open from spring to fall. Maybe a awning over it if prevailing winds could blow the rain in.
Transom Windows...
Your tree will be fine. The only way you would hurt that tree is if you piled used bedding around the trunk, and your not doing that. The root system is well established and even if the gals scratch up a few areas, it's not going to hurt anything.
I don't consider wildlife doing wildlife things when they are actively trying to get into my coops, stressing my birds out. There's no way a coon, mink or anything but a bear is getting to my flock. But stressing them out isn't ok. I've had a pair of fox running around the coop trying to figure...
I agree with most of what you are saying, except for feeding the things.
Also most of the .25 cal air rifles are just about as loud as a .22lr, so a suppressor is recommended.
That's called giving advice. Sometimes the majority of the advice given isn't so popular with some. I gave advice on the information that was provided, not my situation as you accuse.
Your correct, we don't know the exact situation the OP is in. It's up to the OP to gather info and decide...