You are referring to the en passant rule, which means "in passing". As you stated, your pawn must be on the 5th rank, and the pawn you are going to capture must be on an adjacent file. For instance, if you are white and your pawn stands on e5, your opponent's pawn must be on f7 or d7.....if he then advances one of these plaws two squares (f5 or d5) then you may capture it as if it had only moved one square, that is if it was the "f" pawn that advanced to f5 you would put your e-pawn at f6 and remove the black pawn. You can only do this on the NEXT move. If you wait a move, you forfeit the right to this sort of capture. Also, your opponent's pawn must be moving for the first time. If the pawn was on f6 and moved to f5, the move is impossible.

Your plan is correct.....Nbd2 -f1-g3 and black is forced to decide whether to exchange or not on f3. A more common line after 6. h3 used to be 6...h5!? although Fischer analyzed this to a slight advantage to white after 7 d3! (not 7 hxg4 hxg4 and Black gets a very strong attack).

Castling kingside is indicated by 0-0. Queenside: 0-0-0. They're zeros, referring to the number of spaces between the king and rook.

You answered your own question. Until chess is televised don't look for too many of the top GMs to be making the big money. I can see it now, Alex Shirov doing commercials for Gingko and Vitamin E. Karpov doing TV adverts for Head & Shoulders. I'll do underwear commercials ("I checkmate more opponents in my BVDs....").