i understand that when you deflect the rudder to the right or left the corresponding wing will dip caused by the reduced lift from the wing being slowed.
Your first assumption is not always true. It depends on the design. My pattern plane does not have roll or pitch coupling with rudder application (or so little it can't be noticed). I can do a 360 degree rudder-only turn without using ailerons or elevator to maintain altitude. And no, I don't use any mixes.