I find the Wiki a little confusing on this subject, so I'm going to give you my 3 minute overview of these topics.
A. Zones. Zones are simply playback destinations for MC. Zones can be sound cards, external DACs (connected via USB, Toslink, coax, etc), HDMI video/audio cards, or DNLA renderers. MC supports many zones, and many zones can be playing at the same time. Zones can play the same thing via zone linking, or different things. For example, you could have music playing in a zone tied to an internal sound card, and video playing via HDMI.
B. DLNA. This gets confusing because there are different types of DLNA devices. MC can be any of the different types, including:
1. Server. This DLNA device has files that it can serve up to others to play. Kind of a media repository.
2. Client. This DLNA device asks a server for a file to play.
3. Renderer. This DLNA device can actually play back the file to speakers or a display.
2 and 3 are usually the same device, but not always. Don't be too concerned about that.
Typical DLNA playback scenarios:
1. MC "push". From Media Center, you find a DLNA renderer in the left navigation area, under Playing Now. You click it to select it as a playback zone. Then go find media in your library and double click it to play. MC then sends the media over the network to the DNLA device for playback.
2. "Pull" from a DNLA Client/Renderer. Using the interface of your TV (or other DNLA client) you navigate your network to find Media Center. Media Center presents views to show you the media it has. You pick something and press play. The TV (or whatever client you are using) then pulls the media from Media Center and plays it.
3. This is just like #1, it's just controlled in a different way. Using JRemote (or other remote control program) on an ipad (or phone, etc), you pick the media you want from Media Center. You also choose a zone which is a DLNA renderer (this could be your TV, or another device). You press play and MC sends that media to the renderer for playback.
About the network, firewalls, etc.: On most home networks, you won't need to do anything with the router. As long as your devices are all on the same network, they should find each other. However, the Windows firewall can get in the way. I honestly have very little experience with this part (firewall config on windows). If it doesn't work, try disabling the firewall as a test. Note that it can take up to a minute or so for DLNA renderers to appear in Playing Now in Media Center. Not always, not with all devices. But sometimes.
Good luck.
Brian.