Hi SusanSam. I can answer a couple questions.
To my knowledge, they do not bring a cart around after dinner for drinks. What will happen is that your waiter or assistant waiter will take your dessert order, and along with that, ask you if you want any coffee or any other drink with your dessert.
Yes, there is a position for the Head Waiter, and that is one of your staff that you tip at the end of the cruise. Depending on whether or not you prepaid gratuities, you will either get vouchers delivered on the last morning of the cruise by your stateroom attendant, or you can just give cash. The recommended gratuities by Royal Caribbean are here.