Yes, you can get food and drinks on the beach. There are Inn people stationed out there for your assistance. The cabanas are decent sized but there was no competition for seats on the beach (or at the pool) when we were there in late June. Maybe July is more crowded but I don't believe it's much more, as the inn was pretty well full when we were there.
We just stayed (for our 25th wedding anniversary) in the middle of three "rooms" that make up the Lilac cottage, and while the two outer rooms were likely smaller - our center section was a large living room with sofa, chairs, and a small table, with a good sized bathroom and a huge bedroom with ample space around a king size bed. If you get the center section of Whaler, I bet you'll be thrilled with the accomadations. But even if it's an outer room, the Chatham Bars Inn is THE luxury hotel on the Cape. Hard to image there could be a bad room. And the employees are all so solicitous and friendly that they really "sell" the inn. (Did you know you can make arrangements to be driven in to Chatham for dinner, so you don't need to hassle with parking? Great perk!)