
1) The remote control protocol does not allow for remote setting of the hardware offset frequency. There is a gap in the capability noted in https://github.com/gqrx-sdr/gqrx/blob/master/resources/remote-control.txt.
2) The hardware offset frequency, shown as 432 kHz in the screenshot, may be freely set by the user, to any value within the SDR's sampling passband. [A hardware offset is necessary to deal with certain hardware which otherwise shows a spurious peak around 0 Hz due to a DC offset in the signal chain. This effect is present on some, but not all, SDR hardware.]
3) The maximum sensitivity question needs some further clarification.
73
Robin, G8DQX