Alabama and North Carolina do exchange information about tickets and driver's license suspensions. Some states limit the manner in which they assess points for out-of-state tickets, but I don't see an indication that Alabama does so - you can check with the state DPS. You can review Alabama's point system here.

In terms of extra time to pay fines, in my experience it's a case of "You can ask, but you won't necessarily get the time", and that you can often get the best deals (e.g., dismissal upon payment of a fine) by being prepared to pay off the court's assessments. Local law and procedure can vary.