A 5 min tram ride away - Serenity Bay - an exclusive beach for those guest 18+

(1) As we went for lunch we came across a crab in a shell, (2) The lunch setup - included burgers, hotdogs, sandwiches, fruit, salad, ribs, fish, ice cream, cookies and chips:
Some interesting info:

Castaway Cay is a private island or "out island" in the Bahamas which serves as an exclusive port of call for the Disney Wonder and her sister ship, the Disney Magic. The island, located at 26°05′N 77°32′W and formerly known as Gorda Cay, is owned entirely by the Walt Disney Company in contrast to the eight islands leased by other cruise lines for similar purposes. This makes it easy for the company to control all aspects of the "show" put on by the "cast" or employees. The post office even has special Bahamas Disney stamps.

History, construction, and general facilities
The Gorda Cay was once used as a stop for drug runners. The runway on the island was a true operational runway at one point, but since has been used as part of Disney's theme and is no longer functional.
Disney is said to have spent $25,000,000 to develop and outfit the island, topping the $16 million spent by Holland America on Half Moon Cay, and the lesser efforts of other companies. As a result Castaway Cay has the most extensive facilities. Sea water is changed into pure water with reverse osmosis water processors. Construction took 18 months and included dredging 50,000 truckloads of sand from the depths of the Atlantic Ocean. The island is still largely undeveloped: only 55 of the 1,000 acres are being used. Due to the island's expansive insect population, Disney cruises generally depart the island before sunset.
The pier and its approaches were constructed specifically for the Disney ships, so that they could dock alongside easily, thus removing the need for tenders to get the passengers ashore. To create the mooring site for the ships, workers dredged sand from a 1,700-foot channel about 35 feet deep and ranging from 200 to 400 feet wide. The dredge material was used to build the landing island.

Guest areas
Like Disney resorts the island follows a theme, that of a castaway community with carefully planned buildings made to look as if they had been improvised after a shipwreck. However, all the facilities are spotlessly clean, like the Disney theme parks, and the many shops accept guests' stateroom keys for payment much like the theme parks.
Two "submarines" from the closed 20,000 Leagues Under the Sea: Submarine Voyage ride at the Magic Kingdom now lie underwater in the snorkeling area. The Flying Dutchman from the Pirates of the Caribbean movies is on display in the cay lagoon, between the snorkeling areas on the family beaches and the mooring platform for the cruise ships.
As on other cruise lines' private islands, there are no hawkers or panhandlers on Castaway Cay and crowd movement is planned in advance for organized beach parties and other events. The activities on the island are a major source of revenue for the cruise company, since most rentals, such as personal water craft, are not included in the price of the cruise.

Island support facilities and crew only areas
Castaway Cay, like most Disney resorts, has extensive crew-only facilities, with private beaches and recreational areas. Crew Beach is a favorite location for cruise ship and cast employees to relax and be themselves away from the tourists during their precious few moments off. Each department takes turns hosting a lunch barbecue for the other Crew Members on the Crew Beach.
Disney maintains a staff of 40 custodians, boat captains, drivers, landscapers and maintenance personnel who live on the island. They are complemented by members of the Disney Wonder or Disney Magic crew to serve the island's guests when the ship is in port. Food and other supplies are brought in by the ships themselves. Each ship connects to a fiber optic link at the dock to provide data services to the island and allow guests to charge souvenirs, equipment rentals, massages or other purchases back to their cabins.