A: I would say no problem. I use that liquid nails adhesive and I have no doubt that it would hold with only three sides glued.
A: The panel is about 9 3/4 inches square. The opening is about 8 inches square. That extra 1 3/4 inches of the panel is where glue gets applied and then you press the panel into place against the wall or ceiling...centering the hole area.
A: I used standard caulk but you could use construction adhesive.
A: I used liquid nails. My panel is on a wall so it pretty much stayed put once I pressed in into place. For a ceiling you have gravity to deal with so you might need find a means to hold the glued panel in place until the glue sets.