Naturally you asked questions I can't really answer, lol.
We don't eat in the MDR much (my wife is picky and I'm not a huge fan) and didn't use MTD. From what I've read, make reservations ASAP rather than just showing up.
I have never been to the water park (no kids) and don't know exactly when it opens but I do know the line for the big slide can get EXTREMELY long. It seems logical to get settled at your day bed first but my understanding is you want to get to that water slide line ASAP just as you guessed.
I can certainly recommend the food on Cococay. There are snack shacks (one inside the water park) with very good fried chicken sandwiches, mozzarella sticks, and funnel cakes (I've had UK friends tell me they don't know what a funnel cake is, if that's you, google it, then try it, they're amazing).
The other included places to eat are Chill Grill and Skippers Grill (same exact menu). They have a nice taco bar, burgers, hot dogs, some sandwiches, brownies, cookies, etc. They also have ice cream machines similar to on the ship. You can put the ice cream between two large chocolate chip cookies for a wonderful ice cream sandwich.