There is no charge to stay in the dorms. With regard to meals, many of the schools will provide lunch, and some even provide three meals a day. Yes, but only the night before, the nights during and the night the school ends. No, the dorms are not co-ed.
Married couples have to stay in separate dorms.
No, there will not be a chaperone at all times. However, a trained security guard is present and patrols the dormitories every evening. Most likely you will not have enough time to sight-see. The schools last for a full day. If you would like to see the sights, plan to come a few days early or stay a few days after the school ends.