a) The Linux Mint forums
http://forums.linuxmint.com/viewtopic.php?f=46&t=24306&p=142114 say that you can use sudo with your oridinary user password, and then you've got 5 minutes to do what you want. So I guess you could set the root password with
passwd root after using
sudob) As for Earthlink, I've never heard of it. I presume its the name of your ISP and they gave you a setup CD. If your lucky then you've got a broadband router which that CD has already configured for you, and if you're even luckier your router is setup for DHCP.
You could just try using the Linux Mint admin tools to configure your NIC to use DHCP, but if its more complex you might to to boot from Windows again and look at your NIC's TCP/IP Properties, and then boot back to Linux Mint and set the NIC up in the same way.
c) For legal reasons you'll have to download and install libdvdcss seperately before you can play any copyright DVD. There's no law against playing DVDs you've paid for on a Linux machine, but there's debate about whether or not the program that makes it possible could be deemed a copyright circumvention device under DCMA law, so everyone plays it safe and leaves you to install it for yourself.