They do participate in TIW and also have a loyalty program that is great if you dine in Swan/Dolphin signature restaurants at least once per year. www.swandolphinrestaurants.com/loyalty/index.html
No, don't. You can always share as we do. You really don't want to leave anything behind. And if you're still hungry (but I doubt it) there is plenty of food to be had in the area.