Re: Forum types: public, private, hidden
It isn’t possible without some kind of plugin, but it is possible with one.
You would want to take a look at the buddypress/bp-forums/ directory to see how forums are created within BuddyPress to begin with, and modify that existing code in your own plugin to modify that behavior and turn it into what you’re trying to accomplish.
The code is in there to do what you want, you just need to make it do it.