Is the trem in this amp modulating the ac signal at the plate? The LFO is just sharing the preamp input tubes cathode R/C?
No, it is injecting the trem by virtue of the shared cathode resistor.
There is a bypass cap, but trem frequency is down around 3-8Hz, so not much attenuation.
... why the 2 series 510K's going from preamp plate to LFO plate with a .01 cap to ground tap from the 2 510R 's junction. ...
Low-pass filter, mainly to get rid of any upper harmonics the LFO might generate while oscillating. The 1MΩ total resistance pretty well isolates the signal tube from the oscillator.
What
is odd is apparently changing the Depth by varying the plate voltage of the trem oscillator. But since the oscillator causes trem by varying the current through the shared cathode resistor, maybe it makes sense.
Less oscillator plate voltage = less oscillator plate current = less trem current in the shared cathode resistor = less trem of the signal.
There is a multi-section high-pass filter after the signal stage; 0.005uF & 1M are -3dB at ~32Hz; multiple sections roll off more steeply and shift the -3dB point higher. If nothing else, the trem channel is brighter.
The point appears to be to kill pumping when you're not playing but the trem is on high Depth. the low oscillator signal is stripped out, but volume fluctuation of the signal for guitar frequencies is still heard.