The gear you're using is in its own category, just as everything else. I'm assuming you don't use the category tabs when visiting a vendor, and that's why everything you carry (including worn gear) shows. I find it a lot easier to do one tab at a time, that way it let's me skip a lot of stuff if I for example know I only want to sell some weapons and armor. I like that even my worn gear is available, since that means I can compare gear for all my characters, and I can sell worn gear directly if I find an upgrade, instead of having to exit the vendor menu, go into inventory and unequip an item and then talk to the vendor again.
As for the gold, as previously stated it's because of the co-op compartment of the game. They could have implemented pooled gold for single-player, but since single-player and co-op are intertwined it would probably be a bit of a hassle making it work correctly. Just put all the stuff you want to sell on the character with bartering and the issue will more or less resolve itself. Any gold left on other characters can just be sent to that one.
