How do the specific bullet paths and hit boxes work?

It's all about the spray path/kickback of the gun.

The player hitbox is constant (unless you're moving of course), but when you fire any of the guns your next shot will be less accurate. The AK for example has a very accurate first shot, but then that accuracy is gone.

Players will adjust their aim based fire pattern based on the gun. Following the AK example, at close range, after the first two shots players will pull the gun down as the kickback and spray pattern of the gun starts pulling up.

Another example is the sawed-off shotgun. Standing some distance away with your crosshair on the target's head will rarely result in a headshot because of the spray of the bullets. However, aiming slightly below the collar bone on your left as you're looking at them (physical right) will result in one (at least in my experience).

A good way for you to see this yourself is to load up a game, stand and face the wall at some distance and hold down the fire button on any gun. You will see the spray pattern of the gun at that distance. The further away you are, the larger the spray area.

Here is a tutorial regarding the spray pattern in game: