hodgepodge

Hey, sorry if this isn't the right place but I wasn't sure where to put it. I just have a couple questions about using media center as a dvr. Im thinking about buying a tuner card and setting it all up but first I was wondering a couple things.

In my apartment, I have 2 tv's and 2 different cable outlets (no cable boxes either, i go to school and we just have the coaxial sticking out of the wall). In my bedroom is the desktop i want to use but the tv i want to use for it is in the living area. So will I just take the coaxial from the wall to the computer, and buy an HDMI cord or DVI-HDMI cord and run that under the door to the TV in the other room?

Also, when you use this, does it make your computer unable to use other than for TV when watching? and will my nice tv in the living area become the monitor for my desktop or will i still be able to use the monitor im using?

Also, to control everything i will need to be pointing my remote at my PC right? so i may have to step into the other room to change channels, schedule recordings, etc?

Will the sound run through my computer and speakers for that or will it run through the tv?

Lastly, if i decide to get something like a tivo, would you recommend tivo or another brand (preferably one that is less expensive to use). Oh and if you recommend a brand, I don't have high def so i wouldn't need one thats capable. Thanks.