1) if killing rats doesn't work, then try clicking on the rat hole in the tavern cellar
2) you don't need to make him move
3) The switches are to the left and right of the gate behind the staircases and one is directly in front of the gate behind the statue of the guy holding up a hammer
4) see 3)
5) see 3)

These quests are not vital to completing the game anyway. You can just skip them and move on to the Phantom Forest if you want.