Extender question....

What you want is a real "extender". And Xbox 360 is the current best choice for this purpose; you run media center on any PC on your network (yes, you can leave it minimized) and the Xbox connects that PC and gives you the standard media center interface (exactly what you see on your PC when you run media center). You will just need a network cable to connect them both.

Yes to both.

CFC

MCE Extender is built-in Xbox 360.
You don't actually need to have MCE running at the same time you use an extender. The computer itself needs to be running though.

CFC

The way extenders work is that they are a small box that connects via HDMI or Component (for HD) or composite/S-video (for SD - and RGB SCART for SD in Europe) and are connected to a PC running Windows via a network connection. The Windows version running on the PC needs to have Media Center (Windows 7 Home Premium for example)

This network connection between the extender and the PC can be via WiFi (not always that good for HD) or cabled ethernet. If using cabled Ethernet this can be either using a run of Cat5-type cable or in association with something like Moca or Homplug if you can't run Cat 5 for the entire distance between the PC and the Extender.

The Extender can then access any Media Center compatible tuners configured within Media Center on the PC, access any Recorded TV in that PC's Recorded TV library etc. The PC itself needs to be switched on and running Windows (and have a working Windows Media Center configuration) - but the PC doesn't actually need to be running the Windows Media Center application for the extender to work (this happens in the background)

Similar TV recordings will still happen if Media Center isn't running as they happen in the background as well.

The term "streaming" is used to describe playing live or recorded content on a device that doesn't have local storage of that media and is instead accessing it via a network (whatever the network connection maybe)

Well... The answer to your question is:

Get a video card that has dual outputs (and at least one HDMI). An ATI 54XX series would be perfect.

Then, either get a long HDMI cable (<50'), or get a HDMI over cat 5 extender (you'll need dual cat 5 for most of the ones that I've ever seen).

Next, get an IR repeater and run the IR (remote control) signal back from the TV to the computer.

Finally, run 7MC on the PC and put it on the "2nd monitor" (that would be your TV).

However, that said... I don't think this is going to work the way you want it to. It's very easy for media center to lose focus, and also very strange to use a computer with "dual monitors" that have the monitors in different rooms. It's going to be kind of difficult to deal with (things opening on the wrong screen, for example).

For what you'll spend to extend the HDMI cable to the other room, you might be able to buy a small PC to put there. If you have to go more than 50', you're definitely going to spend more (the HDMI extenders are expensive), you'd be better buying another PC (or an XB360).

I've seen setups like this, but never with the TV so far away (typically in the same room, makes it much easier to deal with issues when they crop up; and they will).

Correct, as long as your computer is also on the network, and is on.

It should be good. What are you going to be using to get the data, TV tuner, cable card?

Yep - the XBox 360 will also work as a Media Center Extender (and has the bonus of supporting H264 as well as MPEG2 Live/Recorded TV for those of us who get HD in H264 not MPEG2!)

For Live/Recorded TV you should see no major quality issues. If you want to stream other video files then things get a bit more complex - but for Live/Recorded TV it's great. You also have the bonus of there being a DVD player in it!

Doesn't matter a bit. All is done through the PC.
Enjoy it.
CFC