The first thing I looked at was the roofline. It appears straight in the picture--that's great news. If you have a solid roof the rest should be in good shape, too. So, here's my two bits:
I'd tear out the nest boxes because they could house mites/lice and if the chickens have been pooping in them you don't want that habit to continue. I'd build one or two nest boxes (with room for more if you expand the flock) right by the door so that you don't have to walk across the deep litter to get eggs. Deep litter is great but read up on it so you can do it well and get some beautiful compost, too.
I'd build a small feed room just inside the people door that the birds cannot access. Make that room your feed storage and egg collection space. Mount water and feeder and nest boxes so you are able to stand in that room and yet access everything easily. I built my coop that way and I love the small space--just 2.5x5 feet big it's just right for one person to get chores done. There are so many times when I need to run in there and top off feed and water and collect eggs while on my way to town and I don't want to head off with chicken poop on my shoes. Besides, you need a place to store the feed anyway, so why not make the feed room right in that nice big coop?
If working on the windows you could make them so the hinges are at the top. If the window opens at the bottom then any precipitation is shed down the window rather than blowing in. However, your windows are quite low down and, ideally, ventilation is above the bird's heads in order to remove the warm, moist air the naturally rises.
You mentioned using tree branches as roosts. I learned the hard way that they have to be absolutely straight/flat. A slight slant and chickens spent all night sitting cock-eyed. Hence, there was lots of bickering to sit on the one truly straight segment. Also, after a few months they'd worn off all the bark so it was too smooth for them to get a good grip. I tore them out, put in 3-inch-wide boards and there's much less bickering now as they go up to roost.