how does the negative feedback work on the princeton, princeton reverb, and champ with cathode bypas

The cap doesn't clear anything. AC still has clear exposure to the cathode.

 

...........?

 

Every cap? Or only ones that are actually connected to ground? Have a second look at where that cap is. It prevents ac from appearing across one resistor. As it's not placed across the one that goes to ground it can do nothing to prevent ac from appearing there.

 

Wrong again. If that was the case there would be no bias between G & C.
The cap insures that the AC signal at junction and cathode is the same. (except for a frequency related phase shift)

 

That bit yes.

This bit no.

The bypass cap ensures that the voltage at the cathode is not the same as at the junction.
The bypass cap ensures that the AC signal at the cathode is (almost) the same as at the junction (with previously mentioned exceptions).