Re: scope power
I guess the whole concept of parallax is hard for people to understand. But I'll try to explain it here. The difference in point of impact for changes in magnification may indeed be caused by parallax.
Any scope has NO parallax for one particular target distance. Unless the scope has an adjustable objective lens system (distance focus for the front lens element, sometimes located on the side as well) the parallax can not be removed no matter the cost of the optical system. Parallax is related to the optical system not being in focus for the target distance. The effect is most noticeable with higher power and most scopes of power greater than about 10x have adjustable objective. But the user must adjust the scope for the target distance.
Parallax exits because the target image is not focusing on the cross hairs but in front of or behind them. The rear lens system (ocular lens system) should be adjusted independent of a target so that it is focused on the cross hairs. When both the objective and the ocular lens system are both in perfect focus there is no parallax error. There is no parallax error at any distance IF your eye is perfectly centered in the scope optical system. The parallax error is only apparent when your eye is viewing off the optical center of the scope.
Typically 3x to 9x scopes do not have adjustable objective (front) lenses but are pre-focus at about 150 yds whereas 22 scopes w/o adjustable focus objectives are focused much closer, like at 50 yds. Scope of less than 10 power probably do not need an adjustable objective especially if the user keeps his eye centered in the scope view.
The trick to getting the scope adjusted perfectly is to view the sky through the scope and adjusted the ocular lens system (rear focus adjustment) until the crosshairs are sharp and contrasty. Only then should you attempt to adjust the objective (front) lens system. You can just dial in the distance using the scale provided or adjust the target image for maximum sharpness. There will be no parallax at that one distance and moving the eye back and forth off the optical center of the scope will verify that the cross hairs do not move on the target with the gun held steady. This is a good way to verify the scope is in focus at the target image distance.
Hope this helps.
As an aside, cheap scopes include poor optical systems where it is possible that the whole of the systems optical center could be significantly off. Good lenses assembled off center makes for a problem scope. Better scopes have both better glass and more accurate assembly. In general, I have found that any scope that is much cheaper than $200 list price is suspect for both poor optical performance and poor mechanical assembly. Both cause problems for scopes. I have all kinds of scopes from Leopold and Burris to Bushnell. I have found for my uses (mostly scopes above 10X) that the Bushnell Trophy scopes are about the least expensive scope that I can buy that has both good optical performance and mechanical assembly. Cheaper scopes just do not seem to cut it for me.