As no-one has answered (yet), here's our general thoughts, but all points need to be double-checked (i.e. caveat emptor).
"I cannot see the TV screen from where the PC is situated."
I seem to recall there's a 5m limit between units for HDTV - but that /may/ be the max length for cable availability. Maplin stock 5m DVI to HDTV cables so suggest you email their techie department to query: [email protected]
"Do I need to run a separate sound cable?"
"How good a qaulity will the images be on a HDTV screen?"
Whatever output the graphics card will support. But it would make sense to set it to whatever is the 'native' resolution of the screen so that there's no need for the TV to do any rescaling. So look for a graphics card with an output resolution to match the TV.
"Do I need any special software?"
Nothing except the drivers supplied with the graphics card. HTH.