Is there noise when there are no plugins loaded, only inputs directly connected to output?
Yes. And it is way louder than it should for an unprocessed chain ! touching the string and the metal piece on the top of the MOD, make it weaker.
Is the noise always present, i.e just after turn MOD on?
Yes, it is present when the mod is in bypass mode at startup.
Is it a constant noise or oscillating noise?
Rather a constant noise. If needed, I can record it and post the sound or an image of its spectral density
What are the gains/volumes values you are using?
Input: -4dB. Output: 0dB
Are you using your MOD always in the same environment, for example your house?
I've used it at home and in a studio for rehearsals. In both environment, I got the noise. It was especially loud in the rehearsal studio (the noise was above the threshold of the noise gate plugin that I use in hi-gain pedalboards, so the noise gate was ever open).
Thanks for your help !