Is it possible to add groups via programming / SQL feeds rather than having the users create them? I'd like to create them and then allow users to sign up for them if possible.
Bob, you can create groups as an Admin through the Active Social Control Panel (Groups).
Since active forums is included in the package can this be done with that module instead or as well?
You can display forums within groups. You can also display forums on their own. I would recommend looking at activesocial.com for a working example. Groups and forums are very different..but connected.
Can the various pieces be added individually as modules to specific pages or is the total functionality a "take all and configure or take none" model?
AS is very flexible from a setup and config perspective. Check out the setup and admin guide.