For 12 hens three nests are enough, but if you want more fine. The only possible problem I see is that they may take up room inside the coop, depending on how you build them, and your coop has the potential to be a little small for 12 hens to start with. You’ll probably need to look at your management techniques and in addition to roofing the run close in an area on a side to for a pocket with the coop, roof, and side to keep snow and wind out so they have better access out there in the winter. You can follow the link in my signature for some thoughts on space.
It sounds like you are planning on making nests 12” square. That’s the minimum size I’d suggest for your hens, but I made mine bigger, 16” x 16” x 16”, and I’m glad I did. I don’t know what your shed looks like or how it is framed, but maybe look at your wall studs and use those to help size your nests, especially if you are opening them from outside. You don’t want studs in your way opening the nests.
I let broodies hatch with the flock. I find the bigger nests help with that. But more for your case, it is pretty normal for two or three hens to lay in the same nest at the same time. If the nests are 12” square they lay on top of each other instead of next to each other.
Be generous on putting in permanent year-around vents up high. It’s not good for them to breathe bad air and they can handle cold extremely well. Don’t worry about them getting cold and freezing to death. The real risk is from frostbite. Frostbite is more likely in an enclosed coop where the moisture from their poop and breathing can’t get out. What you want in winter is openings above their heads so the bad air can escape but any breezes are above their heads when roosting.
The chicken wire on the run is a concern. A big raccoon, dog, or some other larger predators can tear chicken wire. What I suggest is that you use 2” x 4” welded wire for the strength of your run against those bigger animals. Then line the inside lower 18” to 24” of the run with the chicken wire to help prevent a raccoon from reaching in and dragging a chicken out piece by piece.
The nests can go any height you are comfortable with. Some people just fill a cardboard box with bedding and put that in a corner on the bedding. Others hang them high enough so they can reach in there without bending, especially if they have a bad back. People care a lot more about nest height than the chickens do.
The roosts need to be higher than anything you don’t want them sleeping on but as low as reasonably possible. The higher you build them the bigger clear landing area they need to hop down. The pop door needs to be raised above the top of the bedding a bit, maybe even a foot, to keep bedding from getting scratched out of it. It’s more like my adults step up that high to get out more than jump.
The way I set the height of things is to determine how high the bedding will go. Be a little generous in this. It will be higher than you think is some areas because of their scratching. Then position the nests. Then make the roosts noticeably higher, say 12”, yet so they are sleeping below your permanent ventilation up top.
With two roosts, the one next to the wall needs to be about 12” away from the wall and the next one with 12” horizontal separation.
I do recommend a droppings board. One of your issues with 12 hens in that coop is going to be poop management. They poop a lot at night while on the roosts. There are all kinds of different ways to do a droppings board or something similar. You need to cover the area beneath the roosts and extend about a foot further out. With two roosts, that means yours will be 3’ wide.
I have a flat piece of plywood (actually the top of a permanent brooder I built in my coop) that I scrape with a broken handled garden hoe when I need to. For me that’s about every two to three weeks, depending on how humid the weather is and how many chickens I have. My goal is to keep it from building up enough to stink. Some people put vinyl on top of paint it and scrape it every day. Some people build a tray and put wood shavings, sand, or something else in there to absorb the moisture. I’ve used plastic bins from
Walmart to just set under there so they are easy to empty. You have all kind of options, but yes, I recommend some type of poop management under the roosts. In a residential neighborhood you certainly don’t want it stinking. You don’t anyway because it’s not healthy but especially in a residential area.
I’d block off the 6” under the coop (or rip out the floor and let the coop floor be dirt but still blocking it off from the outside.) The chickens can get in that 6” space and just may decide to lay eggs under there. How would you retrieve those eggs or an injured chicken that did not want to be retrieved? If there is not enough space for chickens to get under there, it is a great place for Mama Mouse or Mama Rat to raise a family. Am egg-eating snake could set up residence under there, or just hunt that area looking for mice or rats. There is a lot of personal preference in this, but if the building is raised, I’d want it raised enough so I can see under there.
If you do rip the floor out, I’d consider filling it with a few inches of clay dirt before I considered any bedding to keep water from running in from the outside. I put in a swale just above mine and put a few inches of dirt in my coop. It stays very dry inside.
