Even if the murders took place as you were awake or during the night, the main problem is leaving a "perfectly sealed" room.
The door was locked from the inside. As was the window. The cousin must be dead or the culprit wouldn't leave. There is only one person. The culprit could not leave through a "perfectly sealed" entrance. The only way out of the room is one of the 2 perfectly sealed exits. There are no other exits from the room.
Therefore the culprit could not leave... except they did.
PARADOX TIME!!!! There has to be a flaw in this logic somewhere. Unless Eva is just a troll in which case he/she will soon be receiving a strongly worded message regarding my views on him/her.
Don't let this dis-encourage you. I'm not a genius and I don't pretend to be. There's probably something blatantly obvious we have all missed.