So I finally figured out how to actually play Caravan, but I've run into three issues.
1.) The deck Ringo gives you contains one of every card, so what is the point of collecting any more afterward?
2.) New cards linger in your inventory rather than being added to your deck, possibly because your deck already has one of every card.
3.) No one actually bets against you, ever; you cannot gamble on Caravan, at all.
Am I doing something wrong, or is this happening for everybody?
You might want to re-read the rules of Caravan. You are allowed to have multiple cards of the same suit *only* when they come from different decks. By this, you could have 3 or more different 5 of spades.
Why is this important? Because of the Joker rule: you can remove multiples of the same suit by putting a Joker on any Ace on the table. Therefore if someone had a 9 of hearts starting their caravan and placed an 8 and a 5 on it (giving a total of 22) you could place a Joker on the Ace of hearts (whether they played it or you did) and remove all of the hearts on the table (both theirs and yours). This would really stump them from selling their caravan as they would have to have a 4, 3 and a 2 or Ace. Or they could use a same suit change. Still, the point of the game is to force the other player to lay more cards.
Remember this strategy: if you are in danger of losing, make sure you tie at least one caravan. The game goes on until the deck is spent if there is a tied caravan. Once you are winning bids in the other two caravans remove the tied caravan stack. This will cause your opponent to win the previously tied bid but you will instantly win the game (as it is only played until all three bids have been won).
Caravan is brutally easy to play and is a simple way to make money off people if you know how to play it. Just remember to make sure the vendors that play have a good number of caps in their inventory or they won't be betting much at all. Winning 4 caps is pointless.