Audio noise caused by a micro servo

Thank you guys,
I spent most of last two days reading about de-coupling. It makes sense but I never figured out how
to do it in my case.
If it was only my amplifier it would be clearer to me, but how to prevent noise in PA?
PA has nothing common with my amplifier and my pedal board. But it looks like the noise affects PA through main 240V AC power supply.
The building is old and probably bad electrical system but still...

I think I'll try to run my servo and arduino on battery and see what happens.
Then I'll try to experiment with metal box and shielded servo cable.

What do you guys think about battery as power supply for servo and arduino?

There are guitar tuning systems on the marked which run on the battery.
They're probably controlled by a microcontroller and driven by special servos. They don't affect amplifiers arround them.

Another critical question:
Let's say I run arduino on 9V DC buttery and my pedals are powered by 9V DC switch adaptor.
Can I still connect grounds together?

thanks