As you can see, at the top of my door there's an open panel with fixed glass panes attached to allow airflow through. How should I best seal that giant gap up so that I can install air-conditioning in this room?
I would go the home improvement store and buy the following:
A piece of plexiglass (PG), a plexiglass cutter, some clears silicone adhesive caulk, some painters tape and piece of 220 grit sandpaper.
Cut the plexiglass to fit, Measure and mark your PG and use a straight edge to run the cutter against, this scores the PG and then you can snap it on the score line. Search YouTube for visual tutorials.
Lightly sand the edges of the cut to take of the burrs.
Run a bead of caulk around the perimeter and press the PG into place.
put some tape strips over the plexiglass in both directions to keep it from sliding down or moving for 24 hours.
Gently remove tape, have a beer.