I'd say it would be possible but would be a long term project. There are several similar ventures setup as golf clubs around the country and I think that would be the model to follow. They're set up as a golf club or country club with associated mobile homes or houses and other facilities such as clubhouse, bar/restaurant, tennis courts, playgrounds, beach access etc. To answer your questions;
2) I'm sure there's land somewhere, you need to think about airspace as well though. You'll also need to think about other facilities, remember it's not the pilots you're trying to win over, it's their families! 600m runway would be more than enough for most aircraft types once the approaches are clear at each end
3) No airfield licence required for something like this, planning permission is probably your biggest obstacle
4) Hard to say, if it was diverse enough to not only be exclusive to pilots it may work (i.e. many of the country clubs have members that are not golfers but enjoy the location or other amenities).