To specifically answer your questions, it is really a combination of torque and propwash. As the prop turns the slipstream from it is spiraling back along the airframe and once it hits the rudder it tends to push it to the right. The torque of the engine, really the prop, is another reason and the most correctable.

As the plane slows going up, the rudder looses effectiveness and the torque starts to pull the nose to the left. What you do is add right thrust to counter act this problem which is typically done by adding washers between the firewall and engine mount on the pilots side of the plane, this moving the prop to the right. The thing is you do not want to do this until you have decided on the prop you want to use all the time because changing the prop, even when you stay with the same diameter and pitch, will most likely change the right thrust requirements.

Some people will not change the thrust but add a proportional rudder mix to the throttle that once you are close to a certain point with the throttle, right rudder is gradually mixed in. The problem with that is in any other attitude beyond vertical, the more power you feed in the more rudder is fed in and now you are yawing to the right flying straight and level unless you add the mix to a switch. I find that in competing, the last thing I want to have to do is flip a lot of switches. I have enough to do when flying the sequences to worry about flipping a switch for possibly every maneuver.

So basically, the reason you do not see it in most other attitudes is you have good airflow over the rudder, thus helping to keep the plane tracking straight in yaw.

Go with krayzc-RCU's suggestion and do the trim chart and do it in the order it shows. It's a bit of work and could possibly take 20+ flight to finish BUT you'll be amazed at how well the plane will start to fly