1) Hulk, Dueling Dragons, MIB, & Mummy require you to put All Bags & Loose Items in a locker. That means backpacks, purses, souvenir bags, cameras, camcorders, drink cups, etc. Lockers there are free while you ride. After a certain amount of time (60 mins, generally) then the lockers will charge you.
2) None of the water rides have free lockers. What you can do is get a bag from any merchandise store and put any items in the bags. Take as many as you need. Items will be safe and generally stay less wet when placed on the floor for JP and Ripsaw. On Popeye & Bluto's, there is a plastic covering in the middle that you can place all of your items in. They should still be bagged, imo.
3)For loose fitting shoes, do you mean flip-flops? Any backless shoes can be placed in the mini storage bins on Doctor Doom. For Dueling Dragons, you will be required to either sit on them or place them over your hands. Ride operators will NOT hold any items for you.