I think it is a flat rate for the cabana, not a per person charge. of course there may be rules limiting the number of people you can have. If I had a family of 8 onboard I might rent one for the day - that would be a relative bargain. They should add in free soda, though.
As far as privacy goes, you can completely close off the curtains and they are opague, but there wouldn't be anything to stop, say, a curious five-year-old from coming up and untying it or just walking through the closed curtains.