You seem to have this part right, but since it is a common mistake note that the person who comes in LAST PLACE in each non-simultaneous auction gets the "first player" marker or the "losers token" as you call it, making them the first bidder in the next rounds - let's say it's a consolation prize.
Next, a correction of the previous posters assertion. The rules specifically state:
"Note: The start player does not change at the end of Treasure episodes!"
Edit: let me directly answer your questions!
1. What if there's a tie in the money auction? Can there be a tie? Does each bid have to beat the last bid, or can it just match the last bid?
Players can "just match the last bid" which means they stay in the auction and the player that bid before them (the same amount) will have to increase his bid when it comes around to him again in order to stay in the auction.
2. Does the loser of a money auction get the red "loser" token? Ot does it stay with the loser of the last card auction?