I solved my problem and found a solution !!!
First: thank you for all your advices and suggestions. That shows me, that I am not allone.
Problem yesterday: I was confused, because it seemed to me, that I haven`t enough root rights (if that is possible). Those were my observations:
- Sd Maid and AFWall+ were running under root
- Titanium showed me that it had root right, but didn`t show me my apps
- superuser was running, but superSU not
Today I repeated the rooting. But instead of installing the suggested image by Max_S in his instruction I flashed boot-fairphone-fp2-su-eng-r163.img. And now everything works fine.
My final quesion is: Does anyone know an app to restrict the permissions of the other installed apps? I haven`t found anything in the internet as far as Android 5.1 is concerned.
Thank you