So finally, I found a "solution" for my problems.
As a power adapter I can use a Yamaha PA-130A adapter. It's quite expensive, but at least it works. All other adapters I've tried fail.
For the battery-powered solution I tried 6 * 1.5V Mignon AA batteries (adds to 9V) and that works perfectly for me - using one 9V block battery doesn't work.
So, thank you for your help!