Yes, we've done this, both with cash and traveler's checks. Just put down the amount you'd like to charge against when you check in to your resort. Yes, you can ask for a printout at any time during your stay. When you check out, any leftover funds will be given back to you in cash (even if you put down traveler's checks in the first place).
About the restaurants, it's exactly like using a CC, and just like you described.