How much is whites advantage in this position?

By how much do you think white has an advantage here?

LOL.

White is not ahead here.

White has pissed away his opening advantage by trading away queens.  Black's "losing his chance to castle" is trivial.  Frankly, he'd rather have his king in the center anyway, since white has abandoned his hope of an early mate along with his  queen's suicide.  This is dead even...which, in the opening, is a win for black.

Is white an 800?

You're standing better, but by no means enough to win the game. I don't have an engine, but I'm guessing half a pawn advantage.

White is up a pawn here.  On Kxd8, white has Bxf7, and on Nxd8, white has Nxe5.  While "winning" is a bit far off, up a pawn is a pretty good start.

This is funny, did you look at the position? Read the comments? See that white was a pawn up?

Apparently not.

White would be considered here much better with extremely good chances to win. White will win either the f7 or e5 pawn. 

-Zach Kasiurak

I'd give white a pretty decent advantage after winning the pawn. A plan would probably be Ke2, grabbing the d file with the rook, maybe trading black's bishop, getting f2-f3 somewhere to secure the position.