Edit: A lot of people say, that GWM needs a melee weapon attack, but they miss Jesses point: While GWM requires a melee attack with a heavy weapon, Sharpshooters only criteria is an attack with a ranged weapon (not a ranged weapon attack). Jesse bases his claim on the fact, that a crossbow is still a ranged weapon, even if used as an improvised weapon for melee combat. That’s why it deals 1d4(!)+20 damage. (It works with any ranged, heavy weapon btw., so Longbow qualifies too.) Of course Jesse is playing the devils advocate here and of course, no somewhat sane Walter will allow this in any campaign ever, as it’s obviously not the intention behind these feats. But you could read it that way and that’s Jesses (paperthin) point. Besides: he finds the image of a barbarian running around recklessly smashing a crossbow over everyone’s head to just be hilarious.
No. Sharpshooter (as written) requires an attack with a ranged weapon. Nothing says the attack has to be ranged. I could also use a shortbow as an improvised meelee-weapon and triggers Sharshooter (I’m mostly relying on the fact that just because I’m not using it as a ranged weapon, it still is one). But Crossbow is also heavy, allowing the use of GWM.