I also agree on the gutting. That drywall will cause all sorts of problems for you. Chickens will eat anything. So even if it's not in bad shape now, say it gets wet, then they peck at it, now they are all eating drywall.
I would replace the roof sheeting even of it looks ok. You don't want to worry about having to replace it down the line and the new shingles you just put up. Its not huge so in the long run I'd say better to do it now. That also gives you the opportunity to add a ridge vent for added ventilation.
I have the same issue with water run off that someone mentioned. The run had to go where it is and the roof drips into the run. I'd like to install a drain pipe of sorts but now that the fence is in that will be much harder. My other thought is a gutter to divert the rain.
You could look into windows that already fit the framed opening. Some places have rehab stores or discount stores. I bought utility windows for mine. Nothing fancy. Took the screen out and hardware clothed over the ouside.
You could also share the link to this thread in your state thread. People with similar weather often have ideas from experience.
There's a state thread?? Where is that?