well if you look at my code, you can see that I here have an special delay loop, which counts how long same value from ADC is being read, but as it turns out, that was not enough.
Oh, and as a note, before soldering capacitor, I tried to add ferrite beads onto wires going to buttons - that helped a bit, previously, if issues were at PWM value of 170, after ferrite beads, only values below 80 were causing issues.
So as I can estimate, the issues from wires acting as antennas. This means, for next revisions, I should add spread spectrum modulation, to reduce EMI sent into air, and maybe, even use shielding.