I belong to a number of groups on FB (none of which are related in any way to mental health) and I don't recall seeing the sort of format you're talking about, so I can't help you with that. However, in terms of privacy, there are ways to set privacy controls on groups so that only registered members can see them - it depends on the group.
Go to Facebook and search "open," "closed," and "secret" groups, it will explain.
IMO, you're probably better off using a forum like this one, I can't imagine there isn't one for every type of disability.