No appetizer on the regular dining plan - only on the deluxe. Gratuity is not included on either plan.
One adult TS credit on the regular dining plan is redeemable for one entree, one dessert, and one non-alcoholic beverage, or one full buffet (note that at some restaurants, a meal costs 2 TS credits).
One adult TS credit on the deluxe dining plan is redeemable for one appetizer, one entree, one dessert, and one non-alcoholic beverage, or one full buffet (same as above - some restaurants cost 2 credits).
Children's TS credits are redeemable only for children's menu meals.
You do not all have to eat together. The credits are pooled per room reservation (everyone on the same room reservation will have access to the full pool of credits by using their resort room key card). If you are on separate room reservations in two or more rooms, each room has to use their own key card to pay for their own dining.