As regards the ceiling height, you can see a portion of it when Kirk first sneaks through the backstage area:
After building out that complex, I can only say that we see the ceiling for the gym/theater part. But the adjacent room where the two guys are sparring we never see the ceiling. The back columns of that room extend above and past the initial curve of the theater ceiling which means that room's ceiling is quite different and potentially much higher where an unseen 3rd floor might even be possible...