I have a members group that is free and the default when someone registers. And I have a paid "premium" members group at $9/month. If I want to move a user manually via the ACP into the paid members group so they get those benefits, will they get notifications that they need to pay? Or will they just basically be in the paid group for free forever? 

If you just move their usergroup, then they have no subscription to 'nag' them to pay 🙂