However, If I remove the 10 Ohm resistor, the FFT signal looks completely different and the prominent 1 - 2 MHz signal is not observable any more.
There are two possible reasons for that (in practice you will have both of them in combination):
1) adding resistor affects noise power transferred from the source
2) adding resistor affects noise figure of RF frontend input (it can decrease or increase noise figure depends on exact type of LNA)
So, adding resistor affects both - your signal source and your oscilloscope input noise performance.
There is also third reason for the noise level change (which I think is dominant in your case) - adding resistor turns your installation into magnetic loop antenna which is very sensitive for near field magnetic interference. It's the same as adding short circuit, but adding resistor decrease Q factor of such magnetic loop antenna in comparison with short circuit and it makes it more wide bandwidth.
So far I could not yet detect the source of this radiation.
it can be display of your oscilloscope or any other digital circuit near your installation. You can try to find it by moving your "probe" around room and find location where noise level is increased.