When I was a student I was confused when told in Effets of Controls that roll is followed by yaw in the same direction, than in turning that it yaws the opposite way
I didn't really understand it until I did the instructors course despite Trevor Thom's best efforts.
Most of the trainers used these days have most of the adverse yaw designed out of them, so it is not always easy to demostrate it, as it doesn't last long before the secondary effect of aileron becomes more pronounced and it yaws into the roll.
I explain to them how the yaw is caused by a greater wingtip vortex on the upgoing wing causing it to yaw slightly in the opposite direction to the turn, and this needs to be balanced by a little bit of rudder.
Why does the Tommyhawk pitch it's nose down when you yaw? Because the thrust/drag couple is effected, which makes the nose pitch down as drag increases.
Why do people teach to pick up the wing with rudder in a wing drop? beats me. Get the airspeed back, level wings are not a priority. Some schools teach almost a full spin recovery for a wing drop. All you really need to do is relax the back pressure, and the airspeed will be back in a couple of seconds, then level the wings all you like.