#1 - DMZ is an extra layer of protection. It's not very useful for home user but very useful for corporate users who have 2-3 server that they need to their access restrict from the web but completely open for the internal user. (Ex: Exchange)

#2 Your router might not support UPD forwarding. My (Linksys) do.

#3 Pluging a cable modem directly into a computer should work. But you'll need to do a ipconfig /renew to work (Or can you just shut down your computer, change the cable and boot again)