Steam – Is Counter-Strike 1.6 cross compatible with other platforms

What you're looking for is called remote-console, or rcon. It's built right into the game; to use it, set rcon_password to the same value on the server (in server.cfg) and client (in the console), then type into the client-console rcon <command> for any commands you want to run on the server.

You can use rcon outside of the game, too. The most popular tool for this is HLSW.

You cannot log onto the same Steam account in multiple places or it will kick other computers off. Additionally, I think you are unable to 'double buy' a game (though if you got the same game different ways—in a pack and a la carte, for example—you might) on the same account unless it's a gift.

However, you may be able to launch Battlefield outside of Steam (look in the steamapps folder for the executable) however, and work from there. As you suggest, playing online with the same copy may not work, but a LAN game may. Using one copy on multiple computers simultaneously is a little grey though.