I can't answer the detailed technical questions but can maybe provide some useful guidelines.
Biased hot: Stronger overall output, more lows, not as much clean headroom, more saturation and less cutoff distortion, more even order harmonics, tubes wear out faster.
Biased cold: Weaker, thin, harsh output, Lows aren't as strong, more clean headroom overall, more cutoff and less saturation distortion, more odd-order harmonics, and the tubes don't breakup as fast.
I don't know what the range of the Bias control is, but I would expect 5 to be where the tubes are normally biassed, 0 is colder, 10 is hotter - but how hot/cold is unknown.
The above applies to typical Fender, Vox and Marshall amps where the majority of the distortion is coming from the power tubes, and where negative feedback is lost (because the power tubes are clipping and have no more gain), and therefore damping factor be lower.
For modern high gain amps where most to the distortion is coming from the preamp section, power tube bias can have a very different impact. A slightly colder bias might tighten up the amp, and improve the transient response. Hotter bias might result in less controlled tone and too much muddy bass.
So biasing hotter for blues in small amps and biasing colder for metal in high-gain amps might be something to try.
Bias excursion is caused by distorting power tubes causing increased grid current which charges the coupling capacitor between the phase inverter and power tube, which changes the bias of the power tubes. When the input stops, the coupling capacitor slowly discharges allowing the power tube bias to recover. This could make an amp that is biased hotter, become colder biased as it is pushed further into distortion, changing the color of the distortion. Maybe when the hotter biased power tubes are pushed to the edge of breakup there might be warmer even order harmonics, and better bass. As the tube is pushed harder the bias gets colder, there might be more odd order harmonics for more aggressive sounding distortion, and the bass might be reduced.