To turn the aeroplane, it has to yaw (other than, as billiebob said earlier, in a level turn at 90deg bank angle - but since that's rather hard to sustain it can be ignored!). To yaw, it either has to have some small amount of sideslip, even in level flight, for the fin to provide a yawing force ... or a small amount of in-turn or bottom rudder is necessary to achieve the same effect.
As I said earlier, yaw (not surprisingly) occurs about the yaw axis, which is perpendicular to the other 2 axes and not related to where the horizon happens to be.
Yaw is not required in order for the aircraft to change heading EXCEPT when the wings are level.
A normal turn results from the horizontal component of the lift vector.
Yaw results from BANK when the vertical component of lift is insufficient to balance the weight - the aircraft sideslips and directional stability results in yaw.
Yaw results from ROLL because of differential drag caused by aileron deflection. Differential and frise ailerons reduce this but will only work optimally at a certain speed or angle of attack and (I believe) are typically optimised for cruise speed.
HFD