Thanks Syntek !
I read all your links, it was very interesting.
After reading a lot of stuff I think you are right it is down to either EMI or dirty power noise.
Since we live in the same building my neighbour and I, I suspect power pollution through the ground (since we share it)
To answer your questions, all the tests have done were with only KPA + Guitar +Headphones. The sound that you hear in the video I posted above comes from KPA through a little keyboard amp with just my guitar plugged in. So yes I hear the noise always when the AC is on. In order to mostly get rid of it I need to push the Noise gate to 6/7, which degrade the tone IMHO.
My cables are not the problems I think I use those :
https://fr.audiofanzine.com/cable-audio/proco-sound/Defender/
and I also tried with other cables, cheaper but descent.
I tried to move in my room and in the corridor while plugged-in to the KPA and headphone but the sound doesn't seem to change.
So next will be either to try a Furman (M-10x E for starters ? since I do't think I need the fancy features of the PL-PLUS-C) or a UPS, I don't know which solution is better and if an offline ups could help or if I need to go for a line interactive or online
Or go wireless, I don't like this idea (I am probably too old school, took me some time already to decide to buy the KPA ...), but it may solve the problem ... so i might try it