He did beat Karpov in that tournament
How did Magnus Carlsen defeated Garry Kasparov at age 13?

No, he drew on Iceland. It was not a blitz game. His coach then was Simen Agdestein.
https://www.youtube.com/watch?v=WjEmquJhSas

They played two rapid games, Carlen drew one and lost the other.
http://www.chessgames.com/perl/chessgame?gid=1279168
http://www.chessgames.com/perl/chessgame?gid=1279176
an article from that time:
http://en.chessbase.com/post/boy-meets-beast-in-reykjavik
In a blitz tournament used to determine the pairings of the rapid tournament, Carlsen defeated Karpov (the game was not recorded):
https://web.archive.org/web/20081206082807/http://www.aftenposten.no/english/local/article755806.ece

Kid was lucky. It was a blitz game.
Carlsen is much weaker than the great Soviets Karpov and Kasparov. They can destroy him easily in a match even now.

Here is a link with videos of the games:http://www.chess.com/blog/SonofPearl/video-13-year-old-carlsen

Carlsen was winning in that drawn game, though, but he was dow on time.

Carlsen was winning in that drawn game, though, but he was dow on time.
Thats what he gets for acting all cocky getting up and going to look at other games that had nothing to do with his. He thought he could pull that off in a rapid game against Kasparov. Otherwise he would have probably won and Kasparov would have been humiliated.
Carlsen stood up while the game was still in the opening theory. Kasparov was spending a lot of time there for some reason so he decided to stretch a bit.

Carlsen vs Kasparov in Reykjavík Iceland 2004
First game was a draw. (Kasparov was black)
In the second game Kasparov destroyed Magnus. (Kasparov was white)
On 17 March, in a blitz chess tournament in Reykjavík, Iceland, Carlsen defeated former World Champion Anatoly Karpov. The blitz tournament was a preliminary event leading up to a rapid knockout tournament beginning the next day. In that event, Carlsen was paired with Garry Kasparov, then the top-rated player in the world. Carlsen achieved a draw in their first game and lost the second one, and was thus knocked out of the tournament.
https://en.m.wikipedia.org/wiki/Magnus_Carlsen
Kasparov underestimated Carlsen and had not studied his playing style. Carlsen, however, had likely studied intently the games of Kasparov.

How did Carlsen defeat him at age 13? From whom he was taking coachaing and improve chess very quickly?
He sacrificed his Queen in the "game of the century."
Are we talking about Magnus Carlsen or Bobby Fischer?
(Bobby Fischer play the 'game of the century' when he was 13 by sacrificing his Queen.)

Isn't it amazing how people hear a fact and immediately come up with theories to explain it rather than check to see if it's true?

Not sure if OP is stupid or just a bad troll.
Show us proof that Magnus won against Kasparov, when Magnus was 13.

Not sure if OP is stupid or just a bad troll.
Show us proof that Magnus won against Kasparov, when Magnus was 13.
SAYS THE ONE WITH A TROLLFACE AS PROFILE PIC

Not sure if OP is stupid or just a bad troll.
Show us proof that Magnus won against Kasparov, when Magnus was 13.
SAYS THE ONE WITH A TROLLFACE AS PROFILE PIC

http://www.chessgames.com/perl/chess.pl?pid=15940&pid2=52948
(((VyboR wrote:
Not sure if OP is stupid or just a bad troll.
Show us proof that Magnus won against Kasparov, when Magnus was 13.)))
Magnus drew against Kasparov.