Ceiling – What it is this thing above the ceiling

According to the Technical Data Sheet for Lanco Urethanizer (direct link to PDF), or at least from the way I'm reading it, "Lanco Urethanizer" is meant for external applications where you need to make a surface waterproof.

Therefore if those tenants have used it internally to paint walls & ceilings, they have sealed those services ie Made them waterproof.

If I have the above correct, I believe that would explain why you're seeing condensation on the ceiling (and probably on the walls, especially higher up the walls) ie Moisture in the room can't penetrate the waterproof surfaces, instead it just sits on the surface as condensation.

The answer to the code question is variable according to your location, especially if you're in the US as there will be federal, state, county, and maybe even city codes with which to comply.

Besides codes there's simple common sense answers. I think I understand that the stove's pipe goes up an actual brick chimney, not just exposed through the ceiling, and my answer assumes that. I can't see any reason why you can't run the drop ceiling up to the chimney as long as you use fire-rated materials, that means the tracks, track fittings, and tiles themselves. You should make sure about that for the whole drop ceiling really.