first of all "Welcome aboard".
Concerning your questions:
On many cruise lines, bringing wine our other alcoholic drinks on board might indeed be a problem. However, this depends on which line you're sailing with. Also, please keep in mind that many cruise lines charge a "corkage fee" for your wine if you would like to have it with dinner.
The water onboard is of a very high quality. However, on some ships it is fairly heavily chlorinated, so it might not taste as your water at home. If you don't like that chlorinated water taste, bring your own or bring a water filter. If you don't care about this, you should be fine drinking the ship's water.
There are usually lots of activities onboard even on port days. However, there are often fewer people, so the ship might feel much more spacious. The casino and the ship's shops are closed in port.
Enjoy your cruise!