Yes, you can do multiplayer via a LAN, if you have 2 or more CD-keys.
As for what modes there are, that depends on the author of the module your running and the way you set up the server. The official campaign is designed for single or cooperative play, some modules could be set up for arena style play where players face off against one another, still others could be set up for team battles, or a more story line oriented module might have a good party trying to outrace an evil party on some epic quest.
You can do pretty much anything you could do in a Pen&Paper game of DnD (with the notable exception of causing mortal injuries with a well aimed D20).
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