Congrats on booking a cruise! This may sound pretty simple-minded, but I'm going to suggest that since you have internet that you go to the cruise company web site, look at all the photos, and read every scrap of information. Then follow the link to the ship you will be sailing, and take a look at the deck diagrams. Find your cabin! Then, look at all the photos and read everything about your ship. You can often check out the ports you will be visiting on the cruise company web site. If not, run a simple search and find out about the ports!
As to your questions - - -
Breakfast is basically 3 choices -- the buffet (most popular), the dining room, and room service. I suggest the buffet! There is a huge variety of food, and if you can't find lots of things to please you then nothing will ever please you.
Lunch has the same options as breakfast, plus usually an outdoor grill line near the pool for burgers, hotdogs, pizza, etc.
Dinner has the same options as breakfast, plus on some ships an optional extra-cost reservations-only restaurant. Dinner is the time to dress up a bit and go have a lovely dinner in the dining room before the show or the casino or whatever. There are often ships' photographers, and they take some really nice photos. Smile at the fellow, and the next day you can see your photo and may want to buy it. Or not.
By the way, most ships also have a "midnight buffet", which is an array of some of the most beautiful pastries, etc. you will ever see. They really knock themselves out, so do go at least once if only to take a look!
Pay versus free in the food and drinks area is that with almost no exceptions, food is included in the price of your ticket. (The exceptions are the optional restaurants and special ice cream and coffee bars.) Drink-wise, coffee, tea, milk, and juices are included in the price of your ticket, and are available 24 hours a day in the buffet area. Soft drinks are not included and are an extra charge added to your shipboard account along with a 15% tip. You can, however, purchase a "soda card" which is for unlimited soft drinks on board during the cruise. It can be a bit expensive, so it is worthwhile to divide the cost of the card by the number of days to see whether it is worth it to you. By the way, you cannot treat friends and family on your soda card! It is for you only. Alcoholic drinks are not included in the cost of your ticket, and tend to cost about the same as in any very nice bar or restaurant or hotel. They also add the 15% tip to the bill. With almost no exceptions, cruise ships do not have a drink card like the soda card.
Getting away from the food (which you can eat all day long if you like!), you should know that all of the shows, movies, fitness classes on deck, pools, water slides, and exercise center are all included in your ticket, so go have some fun!
Beyond the food again (keep on munching!), what is NOT included in the price of your ticket are photos, souvenirs, gambling and bingo stakes, spa services, medical services, shore excursions, internet connection (horribly expensive!) and ship-to-shore telephone (horribly expensive!) and tips (which are usually added to your shipboard account at the rate of $10 per person per day for the "tip pool" shared with housekeeping and food staff -- they really earn it, so don't cancel the tips!) You will also have to pay to get yourself to and from the ship. As to telephone and internet, figure doing that on board is only for true emergencies. It's terribly expensive and the satellite connections aren't all that reliable anyway (and you don't get a refund if it conks out while you're on the phone or on line). If you feel you really need to be in touch, ask the crew where the internet cafe is on shore -- it's how they keep in touch and they are happy to direct you.
The Caribbean is not a place you find people getting seasick -- it's very smooth, and the ships are large and have stabilizers. It's always possible that someone will get sick, but very unlikely! (I get car sick regularly, and am often seasick on North Atlantic crossings and in the Bay of Biscay, but never have a problem in the Caribbean.)
Some things you haven't asked but might find useful -- be sure to pack flipflops or watershoes, since the decks around the pools can get very hot and very slippery. USE SUNSCREEN -- the sun is really fierce! Take a totebag, which will be good for carrying sunscreen, a cheap paperback, sunglasses, the daily program, and your ID/key on the ship. Don't bother taking an iron -- it's a fire hazard and not allowed in your cabin. Don't take a hairdryer, since that is provided in your cabin. Don't take perfume, either. A cruise is your chance to stop by the shop on board and try the testers. You may find something lovely that you will want to purchase on shore! Don't take heels or hose -- there is a LOT of walking, and you will be a lot more comfortable