No. As long as you can open and shut the doors properly it will be fine. Locking is not part of the MOT. Tell the MOT man or he may lock it!
Stick a hasp and padlock on it : P
No unless they have changed the rules
no
My MOT is up next month. I don't lock my car because if i do i can't open it. It is a 2000 Ford fiesta. So there is not much chance of someone nicking it. lol...Could it cause an MOT fail.