Roost space – They don’t take up a lot of space once they are on the roosts, but they need room to get up there. They spread their wings when they jump/fly up so they need room to do that. They also move around on the roosts to sleep where they want, based on the pecking order. In hot weather they like to spread out, in cold weather they will huddle together. You’ll have different flock dynamics in a flock of 15 than a flock of 4 or 6. If you ever plan to integrate, extra roost space is really beneficial.
Bullies can be at their worst on the roosts. Sometimes you will have a hen that picks on weaker flock members as they are settling down to sleep. With a flock the size of yours, they will segregate on the roosts, different groups sleeping in different places, usually the weaker getting as far from the stronger as they can. There may be more than two groupings up there. Usually a mature flock is pretty peaceful, but not always. When this behavior is worst is when I am integrating younger chickens. If the bullies are brutal enough, the weaker may abandon the roosts and seek a safer place to sleep, often in the nests. The more chickens you have, the less space per chicken you need because more free unused space is available.
The way I suggest you determine your roost space is to look down the road at how many chickens you may have in there at one time that are 12 weeks or older. That’s when my brooder raised chicks normally start to roost, though I’ve had some start at 5 weeks and some wait for months. Then figure 9” per chicken. If you only had 4 chickens I’d suggest maybe 12 per chicken, but you’ll have a minimum of 15. Then look at how wide your coop is and put enough roosts all the way across to give you that as a minimum. Separate them at least 12” horizontally. A bit more won’t hurt anything.
I agree making the roosts removable or hinged where you can swing them up out of the way is a good feature. There are a tremendous number of different ways to do that. I drilled holes through my tree branches and the supports and use a large nail to hold them in place.
Nesting box size and height – For your breeds I’d consider 12” x 12” a minimum. They can use something smaller but for different reasons I like bigger. Mine are 16” x 16” x 16”. It’s not unusual for three of mine to crowd into one nest. If you go with a minimum spacing they are literally laying on top of each other. With more space they can spread out a bit. In the summer those nests can get pretty hot even if they are not on the sunny side of the coop. That’s part of why mine are so high, even though they are not on the sunny side. I have ventilation at the top so hot air can escape.
Another reason I like larger nests is for a broody hen. I let mine hatch eggs with the flock in the regular nests. Often another hen will lay with the broody. More room helps keep the eggs safe when they are maneuvering around. Also, when the chicks hatch, they can be pretty active. Many like to climb on top of Mama. I’ve found that in a small nest, that chick is much more likely to fall off of Mama and out of the nest. With more room, Mama is usually not that close to the front and the chick falls into the nest, not out of it.
I also like a high lip on the nest. With a low lip, the hen can scratch out bedding, fake eggs, or real eggs when she is rearranging the nesting material just the way she likes it. That stuff needs to stay in the nest, not on the coop floor. Again with broodies, it keeps the eggs from being scratched out on the coop floor. It also helps keep the chicks in the nest when they hatch. With a taller lip, you can put more bedding in there to cushion the eggs. I like a minimum of a 5” lip, but again a bit more won’t hurt.
Ho high do you put your nests. That is your choice. Some people put a cardboard box or a bin of some type on the floor and call that good. Some hang nests up as high as they want. If you have a bad back, that may be shoulder height. Look at your convenience more than the convenience of the chickens. Chickens tend to care a lot less than people.
Try not to create a safe place for the chickens to lay under your nests though. If you raise them, raise them high enough so you can see under there in case a hen decides that is a safe place to lay. I’m a firm believer in the value of a fake egg telling a hen where to lay, but some will still want to lay somewhere else, maybe in a corner or even where shadows look like a concealed place.
I’ve had full-sized hens, Australorp, Delaware, Orpington, use an opening on a nest 6” high, but that is fairly tight. Especially with your Brahmas I suggest a minimum of 8” above your lip. That’s another reason my nests are fairly tall. When figuring that opening, watch how you frame it. A brace across the top might eat into your available space for that opening.
Pop Door – I’ve had a Midget White turkey use a 12” x 12” pop door. Your Brahma’s could easily use that, but I’d consider it a minimum. Bigger does not hurt or you can use a people door if you wish. One thing I’d consider is the bigger it is, the more likely rain is to blow in. Whatever you decide make sure you lock it open. You don’t want the wind to blow it shut and lock your chickens out. You also don’t want the wind to slam a door shut when a chicken is standing in that door.
My pop door is a bit over 12” from the coop floor. That way the chickens don’t scratch the bedding out into the run. My chickens don’t even jump up that high, they pretty much just step. If you have a broody raising chicks, you can build a platform inside and out so they can jump or stack bricks, cinder blocks, something like that.
Height of Coop – Pretty much what Aart said, figure out the height of your bedding, then position your nests. Then put your roosts at least 12” above anywhere you don’t want them sleeping, which is usually the top of your nests. Then put your ventilation at least a couple of feet above that so cross-drafts don’t directly hit them in the winter when they are roosting. With 15 or more chickens, you will want a walk-in coop anyway so you need to be able to stand up without hitting your head. Another advantage of a higher coop is in the summer with ventilation open at or below roost height you get a much better cooling effect. Heat is much more dangerous that cold. They need to cool off in the summer.
That’s enough typing this morning. Remember, this is all my opinion based on my experiences. Others will have different experiences and different opinions. Try to pick what sounds like it will work for you. Good luck!