Most cruise lines offer programs for children. Many offer special teen and pre-teen scheduled activites. It is unlikely that you will notice any motion on a large cruise ship, even if you are sensitive to motion in automobiles or airplanes. All ships today have stabilizers to smooth the ride.
Some cruises sail calmer waters than others.
Caribbean and Alaska cruises enjoy smoother sailings than say Bermuda. If seas do get rough, there are many preventative medications available on board. Tipping is up to you. Other ship personnel can be tipped at your discretion. Any state government issued drivers license or other form of picture identification should be acceptable.