Alright let me explain what went down here.
1.) The red truth said Catherine and Edward could not see any way out other than the door and the balcony door.
2.) This leaves room for things they failed to see.
3.) There are paintings of any size in the room. Those could conceal another door. Alternatively, if the door counts as an object that has to be mentioned, the door itself could have been painted on to make it not look like a door.
4.) It was their first time inside the room, so they wouldn't be aware of what the layout was supposed to be.
5.) Alice went into the room with intention to get dressed.
6.) She was explicitly still wearing the same clothes when found and no other clothes were inside the room.
7.) Makes sense if there was actually a closet or bathroom connected to the bedroom though.
8.) Bertrand realized this because he's been there before and went back to get shot by the killer.
Deborah prepared a mercury replica of the Argos Engine with the card inside. She likely used the 3D printer to accomplish this. This was placed inside the temperature-regulated case and stayed all cool and solid. That way, she could slip out the real thing way beforehand and didn't have to worry about it. The EMP deactivated the electronics keeping the case all nice and cool, so the mercury melted and vanished through the holes into the ventilation system. (If the EMP device was too far away, there simply was another hidden closer to the case,
for example inside the cake.
Counter this moooooove.