You choose which weapons you hold onto, you can put he rest in your vault in the tower. You can vary a set amount of items in each category, and the rest can be put in the vault in the tower. Note you can use these items in your vault on all of your characters. I believe enemies drop loot. Don't quote me on that tho And to level things up you simply use them. You want to level up your super, use it. And I don't believe there are skill points per-say but the more you play the more you jump, run, and shoot the more those skills advance toward the next unlock