We have installed a stretch ceiling, but the chandelier is not yet installed. When we open the door and cold air enters the room, there is a silhouette of a square at the place of attachment (visible in the photo). I understand that this is some kind of support, on which the chandelier is attached. Is this how it should be?
You have gaps between the rough ceiling and the walls, respectively because of the pressure drop your ceiling can either stick to the rough, or on the contrary inflate. The problem can be solved by installing small ventilation grids in the stretch ceiling. They will compensate for the pressure and the ceiling won't sway so much.
The support is fine, but you have air coming in between the rough ceiling and the stretch ceiling, and it should not be like this.
That's right, you have a "leak" of air. Either find out where it's coming from (the joints between the panels, the hood, or a hole in the main ceiling) and fix it, or you need to install ventilation grills. Better the former, so as not to make unnecessary holes in the ceiling. Do not hesitate to call where you ordered the ceiling and consult.