R and C wiring for Air Handler and Zone Panel
You should wire this controller according to its documentation.   It's pretty clear.  Each thermostat needs R, C, and the other control wires connected to the appropriate zone terminals.  Each heat/cool/fan device needs its own R, and all the rest of its own signal wires except C to be connected to the appropriate terminals.  Exactly per the documentation.
It seems that the only actual question you have is whether you can skip the R wires from the pump and blower to the controller.  You cannot.  Yes, they have their own power supplies, and it is via the R wires and the controller that those power supplies function.  The controller looks like a thermostat to each of the pump and blower, and needs the R wire just as if it was a thermostat.   The controller doesn't need (and has nowhere to connect) C wires from those devices because it doesn't need their power for itself.
It might help you to imagine the controller, simplified, as nothing more than a light switch, on/off, that controls the pump and fan.   In the case of the fan the &quot;light switch&quot; just connects the R to the G wire.   It can't do that if it doesn't have the R wire!    Unlike the thermostats, it doesn't need that R (and C) wire to power itself, but it still needs it to do it's main task ... turn on the fan.