Hi Matthias,
sorry for the late re-answer.
By the way, we might use German :-) because this seems too specifical for the community ...
Anyway, I'll go on in English until you tell me to stop ...
Basically, my suspicion is that you didn't save your roles along with the option "Change Existing Objects". Only then, the permission settings of a role are "rolled out" to objects which already exist.
Another suspicion is that those tests are inside some courses or groups.
Please remember that courses/groups are protected areas only accessible for their members.
Thus, ILIAS cuts permissions for all roles existing outside the course/group, unless these roles are "protected".
Maybe these are the reasons for your problem.
Still, I don't think you need didactic templates.
In case the problem remains, let me know.