Question 1: Yes:
You can Search police cars more than once per game. Draw cards until you find a weapon. Discard the other cards. The Aaahh! card triggers the appearance of a Walker as usual and interrupts the Search.
Question 2: I would say no, because the objective is to find the violet key, not open the violet door. You'll probably want to repair the damage and lock the door if you're going to hide out in the prison.