Any Marriott owner staying there or exchanging in gets the golf so long as they use a Marriott to get there. I can't use my foxrun week to trade in and get golf even though I'm an owner at Manor Club.
A studio gets you two rounds, 1BR gets 4, and 2BR gets all six.
You can only play two rounds per day, so a foursome is out of luck. You pay $30 pp for the cart (mandatory) making it "not free". When I was there in July the Marriott guest rate was $60 per round including cart and a much smaller amount later in the day (twilight). $60 per round is a very good deal in Williamsburg where the better courses command over $100. Basically the free golf saves you $180 for the six rounds.