rudder

I hope this forum can settle an ongoing conversation with my A&P... I've owned an Archer for 3 months, and the rudder trim has to be adjusted all the way to the right (clockwise) in flight and on stands to make the rudder straight and the pedals aligned. I've asked, is this a rudder rigging...

My new flight instructor told me that the nosewheel on the Piper Archer III we are flying does not turn in flight along with the rudder. I was skeptical of that and after searching around I have found many posts on the web indicating that the fixed gear Pipers do not have nosewheel centering...