First of all, outstanding profile picture!!! We are a big Phineas and Ferb family, and some of our favorite episodes are about Doof and Vanessa. We had a beagle named Buster, but we often referred to him as Doofenshmirtz Beagle Incorporated. So. . . major props for the Doof picture. That's enough backstory for now. . .
But as for your actual post. . .
Are things the same for the most part?
Much of your experience will be the same as what you remember from 2002. (My family's first cruise was on the Wonder in 2001.) Your family will be "introduced" upon boarding. Rotational dining is the same. The featured evening show is still performed twice, so that you can see it whether you have first or second seating for dinner. The basic layout of the classic ships is almost exactly the same, although many of the spaces have been re-designed. If you're on the Dream or Fantasy, then the layout will be much different from what you remember. There are still lots of character interactions, both scheduled and random. There are still fireworks during Caribbean itineraries. (No fireworks in Alaska or Europe.)
The kids' clubs are still free and available to kids from ages 3-18, and the nursery is still available for an additional fee for kids under 3 years old. The clubs themselves operate differently, as adults are not allowed to come and see the kids anytime they want. (There are "open house" hours when adults can come in, but other than that, they've tightened up the entrance rules.)
Castaway Cay day is pretty much the same as it's always been. There's a family beach and an adults-only beach. However, the family beach has been expanded (to accommodate the larger passenger capacity of the Dream/Fantasy). Lunch is still included on Castaway Cay, although as you mention in your post, drinks are extra. The kids' club still operates on the island, as well. One change on Castaway Cay is that there are now private cabanas available to rent for the day. But they sell out fast, so you should not expect to get one (unless you're in a Concierge stateroom).
One big difference is that some of the very popular character interactions now require a ticket. There's a "Princess Gathering", where you can meet 5 princesses at the same time; and there's a Frozen character interaction. You have to get a ticket to be part of these. The ticket is free, there's no charge, but it's how they control the length of the line.
Another change that is near and dear to my heart is that Palo serves brunch on sea days. Soooooooo goooood!!
I remember it just being an all-inclusive trip (minus the booze or purchases).
It is definitely NOT an all-inclusive vacation. While most food (rotational dining, quick service on Deck 9 or Deck 11, snacks in lounges) is included in your cruise fare, there's a LOT that is not included. Alcohol, premium coffee drinks, shore excursions, gratuities, souvenirs, Remy/Palo, photos, spa treatments all carry extra charges.
Am I good to tell the kids, when it comes to food/drink to just ask for it and ye shall receive?
For the most part, yes. As I noted above, there are some food items that carry extra charges. But in the rotational restaurants, or in Cabanas (buffet restaurant), or at the quick service dining on Deck 9 or 11 (including soft serve ice cream), the food is included in the cruise fare and you can ask for as much as you want. Be warned some items on the Room Service menu do carry additional charges.
How late are the non-main dining rooms open until.
Quick service dining on Deck 9 or 11 are usually open until 10 pm, I think. (Might be 11 sometimes, but I feel like it's usually 10.) Cabanas also sometimes serves late. Room service is 24 hours a day.
Younger one may be hungry eating off the kids menu.
Here's a tip. Have them order from the adults' menu. Why not?? My daughter loved chicken fingers and fries as much as anybody, but when we were in the rotational restaurants, she ordered from the adult menu from a very young age. She appreciated good food and she was a little adventurous when it came to food so she was willing to try some things that she wouldn't normally get at home. Definitely made for a great experience for her.
Ok, hope I didn't overshare. Now back to "Night of the Living Pharmacists"! Lots of me. Lots of me!