when running netstat on Windows I see that the following IP address is used: 0.0.0.0
Some TCP and UDP ports are open on it. I've read somewhere that it has to do with DHCP, but why is it listed there and why are there ports open on it?
Well, that could be. But 0.0.0.0, or any address, has nothing to do with a particular device. It is just an address. 0.0.0.0 just tells you where your default (if it can't go anywhere else) route is (could be a cisco router, linksys router, Sonicwall router, linux box used as a router).
Route print (on a Windows machine) will tell you all the routes that that machine knows about. This is set up when you set your networking. The 0.0.0.0 address is the address you will get if you added a default gateway in your TCP/IP setup screen. If you left that field blank - you would have no 0.0.0.0 line.