I always bring a backpack, but I also bring a lot of stuff, and want my stuff. I've tried the fanny pack, and it doesn't hold everything I want/need. DH always uses a fanny pack, or cargo shorts.
It can be somewhat of a pain to squish the backpack down to fit in the lockers, but I'm used to it, and it's not a big deal. Just takes a few more mins. But, I do have to not overpack, make it too full in the middle, as it won't squash enough to fit. I usually have to take out my water bottles, or the refillable mugs for that. I use the same large backpack that I use at Disney. DD uses a mini backpack.
A few rides, you have to put everything in lockers, including backpack or fanny pack, or stuff in pockets, all go in lockers at VC, Hulk, and RRR. Then at MiB, Gringotts, Forbidden Journey, and Mummy, I just use the lockers for my backpack.
Yes, Universal has refillable mugs for in the parks. I plan on bringing 1 or 2 this coming trip, although my son and I just drink water, either bring our own bottles, refill them while in park, but DH prefers soda, etc. Can get water refills at the freestyle machines, or I actually just drink/refill from the water fountains.