1. Is a dvi cable the preferred method to go 35 feet from htpc to plasma?
2. I want to have the audio go from the htpc to both the surround sound as well as the plasma, so we don't always need the surround sound cranked. Is that possible?
1. It depends on what you're feeding the signal to. But, a digital connection will give you the benefit of no signal loss or interference over a longer run.
2. It depends on how you're sending the signal. If you're sending multichannel analog, just put a splitter on the front channels. If you're sending a digital (optical or coax) signal, you'll need to ensure your sound card can ouput analog audio at the same time. Assuming yes, just run the front channel to the TV.
We'll need more info on your setup before giving any specific advice.