Yes. They won't let you carry anything on that doesn't go in your pockets. A fanny pack with a 3 prong clasp is the only exception. Hulk and RRR don't let you take anything at all just your express pass or a lanyard everything else has to go in a locker.
Spike, I don't think they do a week price. Daily, and does not have to be consectutive. Not sure if refill price gets an AP discount, but doesn't hurt to ask. I've only used the regular $1.29 or so, refill when I want with just a plain mug, rather than the Freestyle one. I do, usually get the not Freestyle one with an AP discount, but not usually from the kiosks, mostly in the restaurants.