First Time Cruiser,
1) There is water, juice, lemonade, fruit punch, coffee and tea available all the time in the restaurant. The bottled water are large bottles and I think they are $4. Either bring a plastic container to fill or buy one of the many selections in the gift shop to refill with drinks. There are cards available to buy pop on the ship too. You just show your card to any waiter or at a bar and get the soda of your choice.
2) Other than food or liquor, there is nothing else that I have seen that you couldn't bring back.
3 & 4) All depends on the weather. We were on the Paradise last April and felt it but on the Conquest in December and didn't at all. If you feel at all that it might be an issue, get a patch at your doctors or see the ship doctor on board. I saw many people walking around with the patches.
5) Yep, eat to your hearts content. Order room service too. Just tip the waiters that bring it.
Have a good time.