It sounds like you have a problem in the alternator, possibly a short in it or something, if the regulator is bad in it, it may make your electrical components in the car short out or act funny. If the alternator is going bad, then it would make sense that when you use your electrical components in the car you make the RPMs jump around.
Since you have already replaced the battery, take it to a garage and have them check your alternatori output (preferably when it is acting up if possible) and see if it is putting out too many or too few volts.
