VK, some of your questions can be answered here:
The Villages Health The FAQ and Accepted Insurance pages should be helpful.
At the recent Meet the Developer meeting held by the VHA, Mark Morse stated that you may choose your location and choose your doctor.
Regarding insurance, it appears to me that you may have either 1) Medicare plus many Medicare Supplement plans; or 2) one of these Medicare Advantage plans - Preferred Care Partners or United Healthcare.