#2 is an easy one. The tub for a dog creates very unstable footing. If he shook in the tub, he'd most likely fall, so he doesn't. Have you ever fallen in the tub? It hurts.
#1 I think the best thing for this is for you to take an obedience course with your dog. It will teach you to be assertive and to use the right tone and body language to get respect from your doggy.
Definitely completely stop the game as soon as he starts biting.