Does Uverse use existing TV Coax Cables and wall plates, or does it REQUIRE Phone Jacks, via normal twisted pair phone jacks??

U-verse can use a variety of cables to get the job done.

It can use telephone wiring, a dedicated Cat 5 run, or coax to feed the signal inside the home from the NID on the back of the house.  It can use either coax or twisted pair to deliver signals from the RG to the set top boxes.  The Coax will have to be of sufficient quality and with well-fitted ends.  Your U-verse installer would verify this at installation.

Thanks, but, how do they run the Cat-5, if needed??

It would be pretty difficult to run new cable thru enclosed walls.  Granted, our basement ceiling is all open, giving access to below the walls of the main floor, but, still, trying to run cable, boxes into the existing walls and such would be a challenge??

That is correct bcassill, this is why we depend on the technicians judgement to determine if a new line may be installed. It is not always accessible to install a new line. Coax and Cat5 can be fed into the wall if there are no fire-blocks in the way and there is adequate attic space for the technician to work. The technician may provide other options to install a new line and they will discuss any alternatives with you once they are on site.

hmmm, it'll be interesting...

I want to move my tv and my phone jack wiring is not long alone enough, can I just buy longer phone wiring? Is it a special kind I need?

In the future, start a new thread. This one is 7 years old. 

Are you trying to move the gateway(combo modem/router or the set top box connected to the tv?

If it's not a DVR, consider a wireless receiver. It would still need a power outlet, but it doesn't need a coax or ethernet connection.