The original Dynaco Mk3 has a shared bias circuit for the tube pair. Shannon's design improves upon this with an additional multi-turn trim pot located on the Poseidon board. This allows you to individually set the bias for each output tube. In order that you can measure each tube's idle current, separate cathode sense resistors must be installed.
1/4 watt is plenty. Each tube should draw 70 mA at idle. Across a 10 ohm resistor, you will see a 0.7 volt drop (V=I*R). Power dissipated in the resistor will be only 0.05 watt (P=I*V). If my math is right, the maximum current through the tube should be no more than 186 mA during impossibly loud peaks. Even at that current you'll only burn 0.35 watt in the cathode resistor.
The idea behind the cathode resistors' size is that it will act as a fusible link. If you are continuously running more than 1/4 watt through that resistor, something has gone wrong. Hopefully the resistor will burn out before your expensive output transformer does.
I couldn't say if the screen ballast resistor is necessary. Obviously, Dynaco felt it wasn't required. Then again, I disagree with several of their other design decisions, such as the usage of 525 volt rated power supply capacitors. Many people suggest the screen resistor is a prudent addition, which could potentially extend the life of the output tubes. I have only read one negative remark concerning the screen resistor; it suggested the amp sounded better without it. If I can find the article that promotes the concept, I'll post it here.
Edit - Here it is: http://www.audioxpress.com/magsdirx/ax/ ... ie2544.pdf
Look at the part starting on page 3 under the heading "Simple Solution".
Forgot to answer your first question. My P782 makes just under 900VCT with no load. If you've got a solid state plug in rectifier which you intend to use, the DC rail coming off the rectifier could be as much as sqrt(2)*900/2, or 635 volts.