I checked some things.
- The noise goes away when I roll the volume down on the guitar.
- It is definitely the HB.
- The 5x switch is wired correctly.
Here are some pics.
There is almost no shielding:


The smal metal plate has GND potential. The pots and the 5x switch too.
The humbucker is properly grounded, Its metal case has a connection to GND.
I still wonder why the single coils are OK.. and as the HB is shielded itself, it is a little miracle..?

It is OK for now. I think I add some better shielding next time. What is the best way to do this? Aren't shielded cables enough?
If someone reads this: It's a cheap "Jack&Danny" strat clone.
Volume pot is 8.2K (?), the first tone pot is 254 k, the other 244k... pots and switch seem pretty cheap
