Just got off an Elite on the Dream out of Galveston. Drinks on Us! Anywhere starts when the casino opens in the early evening. You won't get the two bottles of alcohol until the second day. You will have the Elite gathering where drinks will be offered. Our party started pretty early (maybe 4:30 ish), and by the time the hour was up the casino was open. I don't know for sure about drinks from room service, but I would assume they would NOT be included.
Shore excursions offered on mine were:
Option 1: Shipwrecked Castaways: Adult Only Beach - Freeport
Option 2: Dolphin Encounter, Waterpark, Beach & Lunch for all - Nassau
Option 3: Choose your own and get up to $150 per person credit.
I did have to provide a receipt for the parking redemption.