What's going on here?

In the following position:

1. White is winning

2. Black is winning

3. Draw

Although Black's King looks very vulnerable and isolated, and almost all the Black pieces are sitting on their original squares, can White really make some progress here?

Looks like the e5 pawn and white king probably saves black by disconnecting white's major attacking piece, the queen, from the queen side where the action is needed for white. The only hope white has here is check mate or a forced firesale of some black pieces to avoid mate and without the queen's involvement I don't see how that is possible for white. I can't see how black would be anything less than winning with the extra two pieces despite several pieces out of action in the position for the time.

After Qxp white wins a piece....Kxn? Bxb7 disc. ch or...K-b4? a3 ch ...K-a4 N-c3 ch ...K-a5 Bxb7 disc. ch N-a4 mate.However,with ...K-b6 the best I  can see is white forcing a Queen trade with Q-c7 ch(R-c7 might also work here,not sure) ...QxQ NxQ 

Black can safely take the knight after the queen takes on e5.

So Qxe5 isn't a good way for white to play the position. Can't say I have anything alternative to offer for white here at the time though.

For the info, this position result from a variation in a game between Morphy as White vs Anderssen. The variation given for White is indeed erronous as you have correctly answered, and should lead to a Black's victory with proper play. The real problem is White's pieces are way misplaced to be a threat for the Black King and the best White can do is to try to regroup their pieces together. In the meantime, thanks to the open position, Black's Queen and Bishops can instantly jump into the fray to either support their vulnerable King, or trying some counterplay against the White's King depending on the flow of the game.

I liked this exemple so I posted this position to illustrate than a isolated King in the middle of the board is not always losing.

Thanks for participating:)