Is there a movement penalty when starting in the same room as an opponent?
I interpret "moving past an opponent" as walking into a room with an opponent


It doesn't say "to move past an opponent", it says "to leave that room."


  Is there a movement penalty if you are ALREADY in the room with your opponent at the beginning of a turn?


Yes, there's a movement penalty for leaving a room with an opponent. This penalty is not conditional on you having started in another room.


  For example, say I am in a room with 3 zombies at the start of the turn. Does it take me 4 movement points to leave the room (1 for each zombie and 1 as a normal movement point) OR does it take me 1 movement point?


It will take 4 points if you have at least that many. If you have less, it will take however many you have (including none) since you can always move at least once.