Didn't real the full thread, sorry... I'm assuming we aren't using any plywood, styrofoam or glue on the door. And Paul wants it round and opening inward...
If rockwool insulation is permitted, the door would be a lot lighter if it consisted of two wood layers with a 3" layer of rockwool between them. If that isn't ok then it has to be solid wood and it'll be heavier.
Having
enough structure in the wall to support the door is very important.
For windows, I'd suggest a single half circle window on the top half. Then the doorknob can still be centered and the windows are likely available by dismantling a cheap door from the Habitat Restore.
For the hinge I like Paul's sketch on the first page, adjusted a bit below. It would be a shame to have a cool hobbit door with a welded flat hinge on it. I think a little bit of blacksmithing or at least advanced metal fabrication would be in order.
On the right side of the picture is my imagined cross section of the door closing against the wall. No need to worry about the door expanding and contracting if it just presses against a smooth surface. Have a 2-3" area for the door to close and press against. Put felt weatherstripping on it and you're done. The longer the hinge is, the more in the way the door will be. But the easier it is to get the door to seal on the hinge side.
Opening outward would save a bunch of space. And it could be done. Just have the door inset into a 3" larger round hole in the wall. On the inside of that hole have a lip that the door closes tight against. Make a hinge on the outside that jogs around the thickness of the wall to its hinge point. Voila. The door is inside the wall so it will look flush and tucked away and subtle.
For that matter, an inward opening door could seat against a lip that's in the middle of the wall's depth. Then it would look a bit better from the outside (less recessed).