Analysis of Viswanathan Anand vs Vladimir Kramnik in the 2013 Zurich Chess Challenge? I was taking a look at the game between Viswanathan Anand and Vladimir Kramnik in the 2013 Zurich Chess Challenge which can be found here: http://www.chessgames.com/perl/chessgame?gid=1711735.  A few things sparked my interest, one being that I have been practicing the Ruy Lopez, so it was nice to see it played and to put it nicely, Kramnik got spanked, so I was trying to do some analysis on my own, but I am not sure that my analysis is correct and there were some moves that were not immediately clear to me.  Here is the complete game with my analysis questions below:

[FEN ""]
[White "Viswanathan Anand"]
[Black "Vladimir Kramnik"]
[Result "1-0"]

 1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. d3 Bc5 5. Bxc6 dxc6 6. Nbd2 O-O 7. O-O Re8 
 8. Nc4 Nd7 9. Kh1 a5 10. a4 b6 11. Be3 Bb4 12. Nfd2 b5 13. axb5 cxb5 14. c3 bxc4 
15. cxb4 cxd3 16. bxa5 Ba6 17. Qb3 Nf6 18. h3 Nh5 19. Rfc1 Nf4 20. Rc6 Ne2 21. Qd5 Qb8    
22. Rxa6 Rxa6 23. Qxd3 Qxb2 24. Rb1 Rd6 25. Qxe2 Qa2 26. Qb5 c6 27. Qb2



Why was 5.Bxc6 played?  Was the c6 Knight strong at this point
and would this be an even trade?  Basically, why did Anand
trade his light-squared Bishop?
I always hear that you should capture toward the center, so was
there a reason why Kramnik played 5..dxc6 instead of 5...bxc6?
I know 5...dxc6 opens up the file for the black Queen, but that
is all I see.
Is the point of 6. Nbd2 to develop a piece and to add another
defender to the e4 square?
On move 9, Anand played 9. Kh1, but I did not see his King in
immediate danger. I only saw that his f2 pawn was pinned by the
bishop, so is it common practice to move your King away from pins
or similar situations even if they are not in immediate danger?
I don't see the point of 9...a5. I see that it prevents 10. b4. 
Anand followed up with 10. a4 and I see this prevents 10...b5,
but couldn't have Kramnik just played 9...b5 initially?
Apparently Anand sees his dark squared bishop not as strong and
wants to trade it with Kramnik's dark-squared bishop with the move
11. Be3, but Kramnik wants no part of this and rejects the trade
with 11...Bb4.  Can someone elaborate on why Anand wants to
trade bishops here and if it was good or bad for Kramnik to
reject the trade?
I don't get the move 12. Nfd2 except that it adds a defender to
c4 and e4?
22. Rxa6 surprised me as a beginner. To me it looks like Anand is
just giving away his Rook for a Bishop?  The only thing I see is
that if Kramnik captures which I believe he did with 22...Rxa6, it
removes the guard of the d3 pawn allowing Anand to make a skewer
(is that what this is called?) with 23. Qxd3. Was my analysis
correct?
26. Qb5 threatens mate, but Kramnik stops this with c6. Anand
follows up with 27. Qb2 and Kramnik resigned, but it is not
immediately apparent to me why he resigned?  It still looks like it
could have been a draw if Kramnik decided to fight it out. What is
the continuation that I am not seeing?


Disclaimer:  I am a beginner and all answers on this are very much appreciated, so my analysis might not be correct, hence my reason for asking. In particular, my last question about why Kramnik resigned is one that may be apparent to some, but to beginner's it is not, so an answer such as "Black knew he was losing" is not sufficient.  I only mention this because I have asked a similar question before and that is the response I got.  All I am asking for on the last question is a possible continuation.
I'm no pro but I can offer my (potentially incorrect) thoughts.


  I always hear that you should capture toward the center, so was there
  a reason why Kramnik played 5..dxc6 instead of 5...bxc6? I know
  5...dxc6 opens up the file for the black Queen, but that is all I see.


Black gains development of both the queen AND the bishop. It's a free tempi which is important in the early game. I personally choose that much more often than taking with the Knight's pawn.


  Is the point of 6. Nbd2 to develop a piece and to add another defender
  to the e4 square?


Doubt it for e4 nothings bugging that square for a while. I think he wanted to attack e5 or just develop the knight in a fashion where the black bishop couldn't exchange for it?


  Apparently Anand sees his dark squared bishop not as strong and wants
  to trade it withKramnik's dark-squared bishop with the move 11. Be3,
  but Kramnik wants no part of this and rejects the trade with 11...Bb4.
  Can someone elaborate on why Anand wants to trade bishops here and if
  it was good or bad for Kramnik to reject the trade?


I can provide two reasons. If Kramnik takes then white gets to open the file for the rook and has an extra pawn to cover the center. If Kramnik allows Anand to take he has a triple pawn stack. He doesn't like either scenario so flees.


  I don't get the move 12. Nfd2 except that it adds a defender to c4 and e4?


Blocks the bishop pressure on D1, allows white to pressure king side threatening the development of the King's Bishop pawn (which possibly explains the king move as well if he was intending to do that for a while) and the queen.


  
  Rxa6 surprised me as a beginner.... Was my analysis correct?
  


I think so. I'm thinking its the game winning move. It's a fork btw. A skewer is like a pin but the piece of greater value is the first attacked in the line.

The resignation might be to do with his lack of options for dealing with the A pawn. He can't immediately take it due to the potential fork by the knight and white has options to both push and defend it. The only long term solution is to blockade it with one of his pieces and all his pieces are expensive. A blockade would then leave him with a queen and a rook against a queen a rook and either a bishop or a knight on the rest of the board.