Let's see, let me go point by point please.
1. Yes, the broken door you see in Mia's office is a clue that there is something behind the cupboard. You push the cupboard aside and go in. I just tested it and it should work.
2. I still don't fully understand the totality of the bugs you are referring to. I've been checking and what I've seen is that yes, in Main Building F4, the door on the left leads to the music room when it should be closed. I apologize for that, I'll fix it. But the door that leads to the meeting room does indeed lead there. Is it possible that you entered because of the bug in the music room from F4, when you left the music room, you obviously entered F3 because the music room is actually there, then you thought you were actually in F4, tried to enter the meeting room and instead went to the professors' lounge because you were actually in F3? That's the only thing I can think of.
3. Once you get the key, you have to go talk to Yuri in her room and watch the full sex scene. So before unlocking the bad ending, this time the game will ask you to make a decision. Make the right choice and you can continue playing the secret ending.
I hope this clears up your doubts, if there's still something I haven't understood from what you've said, please give me more details.