Let me see if I can break these down one at a time for you.
1.) what is the likelihood to get seasick?
This of course depends on a few things. Not the least of which is your propensity for motion sickness and it depends on just how "rough" the seas are during your cruise. I have cruised 7 times and have never gotten sea sick nor has my wife but I have had friends that cruised with us that did. If you are concerned you can do the typical Dramamine or the little patch behind the ear your doctor can prescribe for you or there is Ginger root if you want to try something natural which has worked for me when I have had upset stomachs. If you do get on board and you feel like you can't get on top of it you can go to the infirmary and they can give you some stronger stuff that will most likely knock it out, though you will be drowsy for a day or so. The ship does move so the possibility is always there but most of the time it isn't a problem I wouldn't worry about it too much.
2.) What activities would you guys recommend for the mentioned ports? Whats fun?
This also depends on a few things. What kind of activities do you normally like to do? Shop, hike, swim, dive, etc.. There are all sorts of excursions, myself I can't stand to just sit on a beach, I like to scuba dive, snorkel or rent a jet ski. I would suggest going through some of the forums dedicated to those locations and just pa ruse them for some ideas, that has proved to be a great resource for me.
Nassau, I haven't really found anything outstanding yet, (I have been there 3 times) but that may be my own fault I haven't really gone out of my way in Nassau. I am sure there are some great dive spots (especially if Shark diving sounds thrilling to you) and I hear the Atlantis resort is a good destination as well.
Half Moon Cay - Great little island, I could snorkel there all day. I also hear the diving is surprisingly good here as well. Since this is a private island the only crowds you will deal with are those from the ship, and there are lots of things to do. This was one of our favorite stops on all of our cruises.
Grand Turk - Not much to say for Grand Turk, it is a very nice island but it isn't very developed in contrast to say Nassau which in a way is nice, the beaches are gorgeous and it is definitely the place to go if you are a diver (have you guessed I dive?
) the reef is awesome. Other than that there isn't much but a few resorts and a big Margarittaville.
3.) What are the table limits in the ships casino? LOL
Can't help you on this one, I haven't done anything more than slots once.
4.) Is the Veranda deck recommended? I heard that the higher up, the sicker you might get....
This is true, the higher you are the more the ship will move, the best location to help alleviate motion sickness is low and in the center of the ship. However, I am still not sure I would worry much about it, I have been on Veranda and I have been on the bottom deck and it really depends on the seas. I tend to look for rooms that are most convenient to get where I am going, Empress tends to be nice on the Fantasy class ships as it is on the same level as the Atrium, but then again I love to go out and watch the ocean so I tend to prefer a cabin that is forward and high up. Again it is all personal preference.
Hope that helps, feel free to ask more questions.