This hen was my slimmest, and determined.
Luckily 2 of 3 doors were adjustable, I narrowed the opening and baited with BOSS, until she couldn't get thru. 3.5" was the limit.
When I first set up my coop partition wall with tiny doors for integrating chicks,
I had a bird get thru a 4" x 4" opening, she was 'slimline' line bird but still.
Will you be using metal or plastic roofing panels?
The members you have under the main rafters should probably go on top of the rafters for purlins to support roofing panels.
Look at 'fly rafters' to extend roof overhangs at end of coop.
Yes, especially if the human access to nests is outside the coop.
Here's some thoughts on heights:
https://www.backyardchickens.com/articles/coop-stack-up-how-high-stuff-works-well.73427/
Learned to... draft on the table, computers, and CADD almost simultaneously.
Spent 20 years making a living with the CADD.
Above the bottom of nest, they want to roost as high as possible.
It doesn't take much height to achieve that.
The lower the roost in a smaller space the better, they need...
Dayum, someone learned to draft 'on the table'!!
Only thing I see that I'd change is making the opening to the nest smaller(12") and thus the lip larger(7").
Oh, and....might also lower nest opening and roost, 34" is pretty high for such a small space.
Roost only needs to be ~12" above bottom...
Not sure why if you have dimensioned illustrations, why you wouldn't post them.
But then I'm a design drafter by trade for decades where dimensions are SOP.