In this scenario, the student is a passive participant in the process. The information learned is impersonal. Clearly, the teacher is in control of the learning process; his or her interests dictate what and how fast the students learn.
The answer in all three cases is that rudder is used to help maintain stability in the roll. A little rudder at just the right time can help keep the nose up in a slow roll or even an aileron roll, as the plane rotates through the sideways portions of the roll when gravity is otherwise not countered.
Typical trim tabs on ailerons, rudder and elevator. Aileron and rudder trim tabs are not very common on light training aircraft. The center console of a small airplane. The vertical black wheel with spherical bumps is the trim-tab control. Moving it upwards changes the 'hands-off' elevator position to a more nose-down position; moving it downwards does the reverse.