I don’t know how cold or snowy your winters might be. How do you plan on closing off that open side, probably wire but maybe something solid? Perhaps we could come up with alternate suggestions that might make it easier or less expensive for you. Putting your general location in your profile can sometimes help with these questions.
You are right, if you elevate the floor and the chickens have access under there it needs to be high enough that you can get under there. With my luck a hen would decide that is the perfect place for a nest.
One concern I have with the floor that uneven, chickens scratch a lot. They just might (probably will) level that floor for you. How will that affect the foundation on the uphill side? You might consider terracing in there. Putting some kind of wall a couple of feet away from that uphill wall or, if I read that sketch right, bring your coop all the way to the ground to limit how much they scratch away from the uphill side. Make a low ceiling walk-in coop with a dirt floor. That would also solve your height problem.
I think that is a great building to use for your chickens, but it does present some challenges.
The progression I use for height is to determine the floor level including any bedding. Then set the nests. After that make the roosts noticeably higher than the nests since they like to sleep in the highest place they can get to. Then put the vents if you use that method. Three feet is not a whole lot to work with.
I’m not sure how you plan to manage them. I see the nests are outside the coop and on the low side. I’m guessing you have openings from inside the coop for them to get to the nests. If you lock them in the coop section at night for predator protection, how early will you be down there to let them out? If you are early enough, do they need access to the nests from inside the coop? Probably so but maybe not. When determining the openings for the nests remember to include any bedding height and in your case, how much they might level a dirt floor if you go that route.
Assuming you build the coop as you plan, the coop being inside that building gives you some opportunities. Instead of having vents under the overhang (if you have an overhang, doesn’t look like it on the upper side), consider putting a larger vent on the wall opposite the roost only for winter. Even with the end of that building just enclosed with wire you should get a tremendous amount of wind protection from the building even if that opening is as low as your roosts. For summer add another vent down low that is open during the heat but closed during the cold. Even if I knew how hot your summers are or how cold your winters are I still would not be able to come up with any magic numbers that are guaranteed to work. How much shade you get from that tree or what are your main wind directions make your situation unique.
I can’t tell if those are 2x6’s or 2x8’s spanning your building. Normally I’d suggest whatever they are, even 2x4’s, leaving that end open and covering that with wire for predator protection. With your height challenges, I’d suggest something like 3” to 4” on the upper side and the full height of those beams on the lower side since it’s protected inside the building.
I’d suggest your roosts be at least a foot below the bottom of your upper opening. Normally I want the roost to be a foot above the nests but in a coop that small 6” might be enough. With your nests external you are looking at the opening, not necessarily the top of your nests, assuming you have an opening on the inside to the nests.
You need to be able to reach everywhere inside the coop for cleaning and any maintenance. An area really important is under your roosts, you may be raking poop build-up out from under there. I don’t know if you are feeding and watering inside the coop or outside. You do not want them pooping in the food and water from the roosts if you feed and water inside. I like having plenty of roost space. With those smaller sized hens (thanks for including number and breed, that helps) you might be able to get way with just one 4’ roost, but especially if you feed and water inside I’d suggest two 4’ roosts on the end away from the food and water (the outside wall). If you do that put a larger vent inside the building on the end away from the roosts.
I really like that building even with the height limits. Somebody is likely to be banging their head in there. I am concerned about them leveling the floor for you. I think you might want to address that.