Black would have the reply ...e3 and things get messy - it's not even clear if White would keep much of an advantage. Bh2 retains complete control and Black has almost no counterplay.

If I recall correctly, Carlsen went on to win this game very convincingly.

In other words, taking the Queen, aka the lady, is not always the right move. This is a part of the depth of chess.

Well, as often happens, it's a double attack when the piece "races" the pawn with captures.  i.e.

Bg5 e3 Bxf6 exd2 with a double attack on the f6 bishop and e1 rook.

Also I guess this hangs the a5 knight, so a tripple attack, and of course black wins one of the pieces.

True, although White wouldn't actually be losing after ...e3 as he can avoid the scenario you mention.

After 1.Bg5 e3 white cannot avoid material losses as after 2.Bxe3 (Bxf6 exd2 -+ was already mentioned) f4 he loses a piece.

Well he's getting 3 pawns for the piece after ...f4 Naxc6 - there's also the possibility of Qxe3 in reply to e3 which is very unclear to say the least.