As has been said before, you can not mail items to your other faction character, that should be basic knowledge to everybody who has ever played on a Normal(not PvP) type realm, where both factions on one account were always possible.
And regarding the auction, even if you could buy your auctions from the same account, why the hell would you? What possible advantage could you gain by it? How would that be any different from having two accounts, one horde, one alliance and buying your auctions that way? It's even more impractical as you can't log onto both chars at once with 2 wow windows and you have to relog all the time.
That is why I wanted borislav to elaborate on what kind of exploits he was talking about.