My issue is solved, but I cannot really retrace how and why...
As I stated in my first thread I'm using a portable version of firefox.
For not making any mess to my running version, I tryied to make a copy for tinkering with it...
... curiously a couple of files were not accessible for copying, so I skipped them. I saw that they were files relating to ABP...
After starting the copy version of Firefox, a message told me that ABP has been installed properly. After that everything (also all other addons) work properly, also ABP, the icon is there, the filter lists work and the clickbox for showing the icon in the addon bar works also. Now I also can find the ABP menu item unter "Extras" ...
Wondrous healing...

The hell knows what was happening there...