What do you tend to like doing? Sit on the beach, do water activities, do cultural tours, eat local foods, do other adventure activities, etc.? People here will be able to more help you if they know what you like to do.
Local vendors are usually less expensive, but Royal vendors give you peace of mind that you won't miss the ship.
There are two different types of Escape Room. The paid one is an actual room and has dynamic pricing, depending on the ship and the sail date and when you purchase. So it will have varying prices. Buy it at a price you can live with and keep checking for lower prices.
Water is available around the ships from large iced containers and cups. If you bring a reusable bottle, you can use a cup to refill it and take it to go. Regular coffee, as @rjweber3 said, is free around the ship as well. And there are a few other free/included options like lemonade or fruit punch, also around the ship in the containers like the water. You don't have to buy any drink package. You can just go with the free and then buy a drink here or there a la carte if you want. The only thing you can't get a la carte is soda from a Freestyle machine because you need the package to get the cup with the special chip to activate it (if you are on a ship with Freestyle).
Cozumel has currents, strong at times. I've found myself working hard and needing fins during Coz snorkeling, even from shore. People who dive here often do "drift diving" because of the currents. There are places right off of shore that have some really fantastic viewing but you should be prepared.
The shows onboard are all included. But reserving in advance is usually necessary to guarantee a seat for a particular date and time. Some ships do this, and some don't.
I don't know anything about the escape room. Bottled water is extra, about $3/bottle. Coffee from the Windjammer, Main Dining Room or other sources is included, except for "fancy" coffee like lattes and such. Anything from Starbuck's is fancy.
I think the Strenuous tag is a liability hedge for Royal. It depends. When I was under 60 years old, I didn't think it was. Now almost 20 years later, it is for me. It depends on your body and condition.
