To understand the final test (different frequencies in the two arms of the phase detector) it is better to think of a phase detector as an RF mixer. The device will output the sum and difference frequencies, these?will be 2MHz and 2842MHz (plus many other harmonically related frequencies). ? However because of the intended use of a phase detector these high frequencies are filtered out so you don't see any output in your test.
To work it will expect to see the same frequency (1420MHz) on both arms. If you put in two signals differing by 1Hz you would see a 1Hz sine wave on the output, but this is very difficult to achieve with the stability of typical amateur signal sources.
In use, the output from the two antennas is at the same frequency and as the relative phase of the signals changes you see a change in the DC output. So to test this connect the same source to both inputs and record the dc output. Then change the length of the cable to one arm This will change the relative phase of the two signals and you should see a change in the output.? Let us know how you get on.