How many nations are able to be played in Sid Meier's hotseat?

The maximum number of players/teams you can have in one game appears to be 12. (Disclaimer: I took these screenshots with the Brave New World DLC enabled; it's possible that this DLC or Gods & Kings DLC added this ability, though I'd be surprised if that's the case.)

I started the game and went to Multiplayer -> Hotseat, chose a "Huge" sized Map, and then clicked "Host Game", which took me to this screen:

(The "Unsupported number of players" warning on the right did give me a bit of pause, but some searching online led me to believe that this was possibly a warning about potential network issues - unlikely, in a hotseat game - and possibly a warning about the unsuitability of the chosen map for the chosen number of players. When I turned off the last 4 players, the warning disappeared, but as you can see below, the game allowed me to start even with the warning.)

I scrolled to the bottom, and as you can see, there are up to 12 teams available.

To answer your second question, yes, you can choose each slot to be for a human, AI, or "closed", so you can give each friend a slot and close the remainder.

Just to verify that it would work, I went ahead and clicked the "Ready" button next to player 1, and the game began. Inside the game it also shows 12 players listed: