Question: Does Gun-Fu only apply to guns? The tooltip just says "does 25% more damage to your second target and beyond in vats" but doesn't actually specify that it has to be guns.

Yes, hence the name GUN-Fu Also, you can read more about it in the http://fallout.wikia.com/wiki/Gun_Fu

By the name, and the gun holding pipboy, I would guess....Yes.

As far as I know it works on any weapon but I don't have gun-fu lvl 3.

There's no explicit gun requirement attached to the perk's effect, but it also uses an entry point specific to Gun-Fu, so there may be a hardcoded (and invisible) restriction.

Easiest way to check would be to get up to the third rank and see if you get the auto-crits with a melee weapon.

No it says specifically "you have learned how to apply the art of kung fu to your guns" so yes it does say it.

Perk descriptions have no effect on gameplay mechanics. I can mod the description to say "Gives you five million health," but it still won't give you five million health unless I make changes to the perk's actual effects.