I haven't stayed at a Ritz Carlton, but I can answer some of your questions. The fee is per room. It sounds like you won't be able to eat breakfast Tuesday morning, so you should tell the front desk that you want to pay for one night but use it for all Monday. That way you'll eat breakfast Monday morning instead of Tuesday. I don't think that should be an issue.

I think it'll be worth it provided you can partake in enough of the food offerings and alcohol. I would be surprised if they let you take alcohol out of the lounge to drink.