Among other things: Low power = wider field of view. This helps with close-up targets or moving targets.
Higher magnification allows more precise aiming at longer distances. It's easier to aim at a particular place on a prairie dog at 400 yards with a 14X or 24X scope, not "just somewhere in the body".
Mirage is caused by heat. It can be from a high temperature and sunshine in the afternoon, or from barrel heating after shots have been fired.
As far as the usual deer hunting need, a fixed-power 4X scope is good to around 350 or 400 yards. That's "need". I've used a 3x9 for decades, but it spends most of the time set on 3X. 9X for sight-in.
You're from BATFE? Come right in! I use all your fine products!