I'm not going through the rest of the thread to see if others have made the same points, so am posting a video soon to cover any SHRA.
Also I'm jotting down thoughts quickly and don't mean to be curt or harsh.
Door:
You want a door that the measurement is 29 1/2" wide and the height is 70". This is because you have a door frame already there that is solid, can hold the hinges, etc., and these are the accurate inside measurements to butt up to that, right?
You can cover one side of this door with one 4'x8' piece of plywood. I would suggest 1/4" plywood, especially if you are doing two sides. This is going to be really heavy with 1/2" plywood, even on one side.
I question your intention to insulate: it makes good homes for mice and mites and you might be ripping off one side at some point to get at and treat them. If you are looking for the cross-bracing qualities of plywood, then at least use corner braces and save the weight. These kinds of doors can warp and flex along the front and back dimension a lot too, where one corner or the other wants to bend toward the opposite corner. This can interfere with the window and pop door fit. You could put in diagonal braces.
Would a Dutch door work, where you hardware-cloth the top part on the inside, and attach a hinged piece of plywood, either on a frame or not, to the outside door frame as a cover? The entire upper part of the door works as a window.
2x2's:
I would suggest 2x2 corner braces on each corner of your door frame, having worked with a ton of 2x2's myself you will really appreciate the diagonal bracing, even little pipeces work really well, see this video, a guy building a coop door
You need to account for 2x2's not being fully dimensional. They aren't even 1.5" at times though that's what one plans for. So your measurement of 25 1/2" for the top of your window, means 22 1/2" or less for the bottom inside 2x2.
I don't have time right now to add up the wood needed and check that, sorry. I can see you need 20 feet of 2x2's just for the outside framing and my recommendation of 2x2 corner bracing.
You want to go through and then halfway in to what you're screwing to. So with 1.5" 2x2's you'll want 1.25" self-tapping wood screws with 1/2" ply (.75" + .5"), or 1" with 1/4" ply.
Whatever you do I think you should plan and build the whole door, THEN cut out for the window and pop door when you make them. For instance - if you do put in corner braces then those might move your pop door in a few inches. So once it's all there you can see what you're working with.