Hi Beech19,
Hydroplaning has been discussed at lenghts in several forums. Try a search for:
Hydroplaning or Aquaplaning you should be able to find the threads.
As for your questions:
1. This formula exists 9x square root tire pressure has been derived as an approximation. As for what I have learnt from the NASA study it is the speed at which you can expect aquaplaning "FOR SURE" to happen.
2. No formulaes for rubber reverted or viscous as these hydroplaning situations are dynamic. Friction coefficients vary from good braking to black ice! So no means of determining it. I had viscous hydroplaning at 70 kt in an Aztec as well as at 110 kt in an ATR.
3. Special techniques - in what aircraft? Worked for me in the past: (Other comments especially from the big jet community very welcome)
Small aircraft: (normally keep directional control and apply the brakes slowly not to lock up the wheels. If it is from reverted rubber then it normally means you are landing on a long runway for the plane. Just keep it on the centreline.
Turboprops: Full reverse (is safety relevant and overrules any noise abatement procedures) and max braking. Go-around might be an option to come in for another approach maybe 15 minutes later when the rain has washed away the slime.
General: Displace your touchdown point if possible. Choose another runway.