This has never happened during playtesting, but theoretically there are some situations where it could. If a player would draw and no cards are available, nothing happens, the player does not draw. If you get to Step 3 of a new round and cannot deal out the exact amount of water or treasure cards. Than move to Sinking Procedures to reset the round.

Yes, if you are playing the card for it's triggered ability, you must be able to complete the ability.

Cursed Amulets are not duplicative of one another. In other words, if you have 4 Amulets cards in your hand, then the total value of all 4 cards is 12 Points.