Hey there, Arka!
Currently, the plugin doesn't allow for custom coding your own pre-defined groups, you might find our embedded form a better fit for that specific need:
How can I add my signup form to my website?: http://eepurl.com/gOGN
However, we do get this feedback quite often, and I'm happy to pass this along to the developers, as well. :)
Regarding Facebook, you've got a couple options! With a release we pushed out a few months ago, MailChimp can now track where some of your subscribers signed up at, including Facebook!
However, if you're wanting to add them to a specific group, automatically, your best bet is going to be to check out an integration called "ShortStack":
They'll let you embed a custom form on your Facebook page, so you can add people signing up there to a specific group.