1. Almost all active items are multi-use items and recharge with damage dealt. If an item has limited uses, it will display the amount with a little number (e.g. the coin has 3 uses, displaying a 3)

2. Nope, not really. Unless you are lightning fast, then you could go around juggling teleporters, but that's probably not worth it. A sell creep would have to have spawned first anyway.

3. Nope, not directly. Though the weapons do correspond to 1-9 (maybe more idk) of your keyboard, with 1 being the starter weapon and then going in the order you picked 'em up. Otherwise you can press and hold 'Ctrl' to more easily select which weapon to choose. No way to take crap weapons out, besides discarding them

4. Not sure about that one. been to long. I assume you are talking about the one in the main hub? It probably refreshes on each completed run (regardless of death or success).

You learn run by run

On your fourth question: The shops in the Breach add new supply in a specific, predetermined order. The only way to get new items in each shop is to buy something, then do a run, which will then refill all emptied slots with the next things in the list.