I wonder how white was able to calculate such advantage before using his rook for a pawn.  The guy must be Fischer.

It's real.

I 'solved' this, but in a real game, I may have difficulty finishing off Black. After Qxe2 Kxf7, what is the best plan to simplify for White? I thought Black is disadvantaged but not hopeless, as there may be chances that White overlooks possible perpetual checks and so on. What do you all think?

Agreed.  This will be a tough win for white as it's hard to find a clear winning plan other than to try to force a queen trade, but white should definitely win.

I dont get why the king cant move to d7 out of check at the last position ... and i certainly dont get why the king wouldnt take the bishop

U-Got_Pawwned, they are assuming the player absolutely refuses to give up his queen. All the movements of the king keep it next to the queen to defend it.

At the end yes, the king will take the bishop leaving white with 6 pawns and a queen and black with 4 pawns and a queen. The result is simply reducing the attacking pieces of black as the rook was in a strong position originally. Now the balance is clearly in white's favour.