If the host drops, another Xbox will take up the hosting of the game, supposedly with only a momentary pause, if any.
It is unknown if there will be any dedicated servers. There will definitely be no dedicated servers for games that are matchmade using XBL's matchmaking facilities.
16 players per game, up to 4 players per Xbox, splitscreen.
You'll enter games through a search and matchmaking feature; there will be no access to comprehensive lists of servers, games, or players. Instead, you create a playlist that includes combinations of features you want included in the game you'll play, and the system finds these and shows you a short list.
However, you can affect Halo 2's matchmaking through your Friends list, which Halo 2 will display, allowing you to send text or voice messages. You can use the Friends list, or a list of players from recent games you've played in, to form what's called a Party, that will last the duration of a gaming session, and allows a group to move from ranked game to ranked game as if they were a single player. Parties can also be merged. The relationship between parties and clans, and how clans fit into ranked play, is not yet clear.
As customary in XBL, you can choose to search for games via QuickMatch, where XBL chooses for you, or OptiMatch, where you get to select certain criteria.