The game is always-online, even for single player or local LAN. Which means you can get lag-killed in single player, or the server is full (which happened at launch) so you can't play your single player game. The game also kicks you out if you lose your connection while you're playing.
postfix, prefix. Gear gets a randomly generated name based on what special properties it has. So the red club of the owl is a club that has added fire damage(has red prefix) and a health bonus(has owl suffix)(or something I only play diablo causally so I don't know the affixes off hand.)