Jumping While Pushing Through Fire Makes A Difference

It scales linearly, and each gun has a different scaling factor known as its RangeModifier. Shotguns scale the worst, followed by SMG's and pistols, then automatics, then sniper rifles.

Lowers damage based on the distance of a target. At 9.525m(500u) away, a target will receive an estimated damage of RangeModifier * Damage.

See the spreadsheet here for more details.

With regards to knives in CS:GO, you inflict the same damage to an opponent with a knife to the head as with a knife to a leg. The extra damage element is caused by knifing from the front/side or the back.

This weapon chart shows the knife damage of the primary and secondary attack, to each hit box area (although irrelevant) and also whether in front/side or behind your opponent. As you can see, the hit box area causes no difference in damage.

Interestingly, this chart shows that kevlar and helmet mitigate knife damage. It also indicates that it reduces the damage when hit in the legs. Kevlar doesn't reduce damage to the legs with any other weapon. This seems to indicate that knife damage is based solely on whether hit from the front/side or back.