There are many fine restaurants and most with outdoor seating. Our favorite is Fishcamp on Broad Creek. Superb food, good service, plenty of outdoor seating, and a lovely ambiance (it sits at a dock and marina)--and they take reservations. Hudson's and Skull Creek Boathouse are both good (like Boathouse better), but neither take reservations so go early whether it's for lunch or dinner...as in really early. Skull Creek Dockside isn't as good as either of the three I've mentioned, but they're solid, and they take reservations. Closer to the resort, you have Scott's just across the marina in Shelter Cove, maybe a 5-minute walk. Outdoor dining, solid food, no reservations. Then, about another 5-7 minutes farther down the marina at Shelter Cove, there is Ela's on the Water. I believe they take reservations and there menu and dishes are very good--but a bit pricier than the others. Finally, I'm a big believer in finding menus you like online, then determining where you wish to eat. You can always call to see if a particular restaurant has outdoor dining options.
As for beach equipment, the resort provides or rents nothing in that regard. You can use the Hilton Head Beach Services online reservation system to reserve yours, though they are pricey. Nevertheless, there is very little hassle doing it that way. Alternately, you can buy your own chairs and umbrellas when you arrive from Kroger,
Walmart, and several other places. Cheaper option, but then you have to get them to the beach. The shuttle can take certain items, but in the height of summer, space may be limited. While there is no priority parking areas at the Beach House, if you get there by 10-10:30 a.m. most days, you will be able to find a parking spot. And generally speaking, by 3-3:30 p.m., the lot starts to empty so spots are available. Finally, you can alway drive over and unload the chair and ask the CMs at the Beach House to hold onto it for you. You could then drive back to the resort, take the shuttle back to the BH, then pick up your chair. That's a long process, but it's an option.
Have a great trip!