Carlsen-Anand, Game 2. Could Black hold if not for 34...h5? At Black's 34th move in Game 2 of the Carlsen-Anand match, Anand blundered with 34...h5??. What were his chances for salvaging the draw if he had defended actively via, say, 34...Qd2 or 34...Qd4, counterattacking the f2 pawn?

[fen "5rk1/4R1pp/3q1p2/p1p2P2/P3Q2P/5p2/2P2PPK/8 w - - 0 1"]
[Event "WCC"]
[Site "Sochi"]
[Date "2014.11.09"]
[Round "2"]
[White "Magnus Carlsen"]
[Black "Viswanathan Anand"]
[Result "1-0"]

1.g3 h5?? 
    ( 1...Qd2 )
        ( 1...Qd4 )
2.Qb7 1-0


I'm looking for explanations of how White should then push for victory, and how Black should best respond, backed up with concrete analysis. Please note that I'm not at all interested in pure engine evaluations, but rather verbal, human annotations of the possibilities (though engine-checked analysis is certainly encouraged).
Anand could have chosen

[fen "5rk1/4R1pp/3q1p2/p1p2P2/P3Q2P/5p2/2P2PPK/8 w - - 0 1"]
[Event "WCC"]
[Site "Sochi"]
[Date "2014.11.09"]
[Round "2"]
[White "Magnus Carlsen"]
[Black "Viswanathan Anand"]
[Result "1-0"]

1.g3 Qd2 2.Qxf3 Qxc2 3.Kg2


After which we reach a Queen+Rook middlegame. In such middlegames, the following factors are critical:


King safety
Piece harmony (coordination and collaboration between the Queen and Rook)


My evaluation of the position above is as follows. Black's King is less safe, since the f-pawn is on f6, exposing the seventh rank for the white Re7 and making it possible for white to attack the g7-square. Further, the white Re7 is better placed than the black Rf8. The white Qf3 is controlling the h1-a8 diagonal, safe guarding the white Kg2 as well as threatening Qf3-g4, Qf3-d5 and Qf3-b7.

White can have the following strategy: use the better King safety and harmony to attack the enemy King and checkmate and/or win material along the way.

Black can have the following strategy: keep the pieces active, try to make them collaborate better, seek a counter attack on the enemy King, try to exchange queens.

I think the position is better for white yet black can still fight. For example

[fen "5rk1/4R1pp/3q1p2/p1p2P2/P3Q2P/5p2/2P2PPK/8 w - - 0 1"]
[Event "WCC"]
[Site "Sochi"]
[Date "2014.11.09"]
[Round "2"]
[White "Magnus Carlsen"]
[Black "Viswanathan Anand"]
[Result "1-0"]

1.g3 Qd2 2.Qxf3 (2.Qe6+ Kh8 3.Qf7 Qxf2+ 4.Kh3 Qf1+ 5.Kg4 h5+ 6.Qxh5+ Kg8=) Qxc2 3.Kg2 Kh8 4.Qg4 (4.Qb7 Qxf5 5.Rxg7 Rd8) Rg8


Conclusion from the position after 1...Qd2:

[fen "5rk1/4R1pp/3q1p2/p1p2P2/P3Q2P/5p2/2P2PPK/8 w - - 0 1"]
[Event "WCC"]
[Site "Sochi"]
[Date "2014.11.09"]
[Round "2"]
[White "Magnus Carlsen"]
[Black "Viswanathan Anand"]
[Result "1-0"]

1.g3 Qd2



Black should play Kg8-h8, Rf8-g8 and h7-h6 to secure the kingside.
Black should trade all the pawns on the queenside and play 3 against 4 on the kingside.
White should try to prevent this from happening.