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You have quite a heavy feature request and requires some thought to answer properly and implement.
We've started working on feature code named "spaces" and need to think a bit more on how this will work with the user groups and how to implement the user interface.
One thing seems clear: we'll have a url specific to space, for example - instead of "questions/" we'll have "productA/" etc.
We don't have yet exactly what you are looking for, but we are working towards that. Realistically this can take two-three months.
Hiding groups to which user does not belong as well as the everyone group is easy.
The "moderator adds users" action can be done by going to a user profile and adding/removing a group on that page.