I was there last summer and if nothing has changed, which I don't believe it has, here is the deal.
You will have to sign for everything at the bars and restaurants as if you are charging it to your room. When you get your bill, you will not be charged for anything. It is a little annoying having to wait to sign for a bottle of water but you will get used to it.
The only restrictictions I recall are the following:
You are limited on the number of times you can eat at their nice restaurant - Davinci's. For a 7 night stay, you can eat there 3 times. For a 5 night stay, I think it is twice. I could be wrong. They have to restrict this because would would probably be tempted to eat there every night. It is hands down the best restaurant I have ever been to at an all-inclusive.
The second restriction is for room service. They will not allow you to order drinks only. You have to order food as well. If you want a few beers, you will need to order some chips and salsa or a pizza.
These are the only restrictions that I am aware of. At the buffet, you can ask for a menu and order al la carte. At the beach restaurant, we ordered triple orders (for one person) of their garlic shrimp with no problem. You can sit under a palapa on the beach and have them shuttle plates of garlic shrimp and of beer on ice all day. It is all included.
That is one of the best things about the Omni. They will bring you actual cans of beer on ice. Every other all-inclusive hotel I have been to will only give you a beer on tap in a small plastic cup.
Don't worry about a thing. One negative is since this is your first all-inclusive experience in Cancun, you will spoiled. You will always compare their all-inclusive program to others and frankly, even the more expensive hotels won't measure up.