Is it possible for the host of a game to switch civs?

Yes, once there are 2 people in the game, if the host wants to switch civs in the middle of the game then the other player becomes the new host.

Hmm, I usually play it direct IP or LAN, since I'm playing with my wife in the same room. I'm guessing your method is for internet games.

Nope. The "host" is whichever computer started the game, and the "clients" connect to the host. If the host leaves the game, a client becomes the new host. Since Civilization isn't really a "real-time" game, the switch is seamless.