US citizens can use birth certificate and a photo ID. I personally prefer having a passport when I leave the country. If you have one, I'd say bring it. There's no pressing need to get one, though, especially if you have to pay extra for expedited processing.
Are they driving from Panama City? Isn't that like a 7+ hour drive? The port opens at 10:30am, boarding begins at around 12:15 or so. I would think they might consider driving in the day before and staying near the port.
On the 7-night cruises, there are two formal nights (actually a "formal" and a "semi-formal" night), and the rest are casual dress at dinner. They request that you don't wear shorts to dinner in the main dining rooms. If they are dining at Palo, there is a "jacket recommended" dress code.
There's some good information on shore excursions at
http://www.dcltribute.com/excursions/.
There are a lot of different meal options. In addition to the three main restaurants, there is Palo, for adults only, there are snacks on deck 9 at Pluto's Dog House and Pinnocchio's Pizzeria, there is room service, and for breakfast and lunch, there is a buffet (in addition to sit-down service in the restaurants). Also on the 7-night trips, you can eat dinner at the buffet for a more casual atmosphere than the main dining rooms.