Yes, there is a doctor and two nurses on board.
If you are afriad of becoming seasick, I suggest that you buy some Bonine and start taking it 2 days before you board the ship, and then take one the day you board. If you are still worried about being sick while on board take one tablet either in the morning or before going to bed at night. Just follow the directions on the package. You can also get Meclizine (same as Bonine) on the ship either in the Infirmary or at the Front Desk - no charge, but I would still buy a package of Bonine.
Can't help you with the weather - no one can predict what it will be like or if you will have calm or rough seas.
Have a wonderful time.