Is it possible to run a server off of a DVD? You can already run Linux off of a CD, so if you make a Linux DVD with all the server files on it, could you run it that way?

It doesn´t gone, because the server write information about Account and char into the Database. If you rún it on a CD/DVD you get problems with the Server and the Database You can use it only with de Server files the Database must be on a different place like a webserver or hdd.

Yes you can.
Load up your live CD and install MySQL. It will install it in memory and then load up your server. Although nothing will be saved when you turn the machine off.

Might be a good way to run a fun server. Raid server. Set all players to a certain way burn it and everytime you play it's same chars no changes.

You're going to need a good chunk of memory then...

Just make a custom Live CD that includes the server. After initializing the CD in memory, you can run the server dynamically from the RAM and you can even save information to a USB stick (Char info, etc..).