Yes,the spike of H3 and the canceling of H2 is indeed weird.
It's maybe related to the speed of the fan as it's just a plain 120 mm,2000 RPM fan,the ones we use for PC cooling and for the shake of the test I powered it with a 12VDC adapter plugged to a different wall socket and just put it on top of the interface under test (an E-MU 0204) .
I have also seen the effects of other motors,LED lights,HVAC,etc if I measure using another electrical line than the dedicated one I have for my stuff (I have 3-phase electrical system in my house) .
In the specific test,proximity of the fan also matters.moving a few cm further i had less interference.
To take it the the very extreme I also tested it with a very strong hair blower,not blowing directly at it of course as it could melt stuff but just beside it and it was really all over the place,the waveform was like severe clipping.
Fans and audio is no good mix for me after that,that's for sure.