So you'll be just fine in Michael's Club with ordering martinis. We went several times, and it is a full bar.
Celebrity will give Elite Members a white card along with your Sea Pass card. The white plastic card has your name, room number and Captain's Club number, along with your status. You can use this card for entry into the private Elite functions. I was never asked for mine though.
Cocktails are from 4-6 PM and you are of course permitted to step outside of Michaels to meander. We (along with other couples) would take our pre-dinner cocktails along to the dining room and it was just fine.
The continental breakfast with brew coffee was great as well.