Hi Bina:
my cat is a male, name is Blackie. hee hee, owner adopting his name. I think you're right - he thinks it's his room! Or maybe he thinks he wants to exchange room with me! His room is smaller, and with all the cat furniture, and cat bed, I bet he thinks it's not fair I get the larger room.
But hey, you're really patient, opening the door at 3am for your cat to get out and then around 4am for her to get back in.

Hi Erin:
No, haven't found any cat flaps locally yet. Will let you know if I find one. Such a useful thing when the furry member of the family decides to be nocturnal.