Okay, already working again.
Now everyone can login with their forum user name and password.
In the DokuWiki configuration settings (accessible by Admins/"super-users"), there are options for assigning certain members or groups as "superuser" or "manager".
The "superusers" have access to all configuration settings. They can change everything. I think they also have automatically access to all Wiki pages and namespaces.
And if I understand correctly, they are the only ones who can set user permissions for pages and namespaces in the "Access Control List Management".
I have made the following settings for testing for now, don't know what would be most practical:
At the moment, "superusers" is set to: "@Administrator,@Administrator (klösterlich),Johann,Danilo"
(Groups can be set beginning with '@', and all names must be separated by commas.)
The "managers" can do some administrative things, like reverting some changes. I don't know what else exactly. But they don't have many possibilities to change global settings and also cannot set permissions for pages and namespaces in the "Access Control List Management", I think.
At the moment, "managers" is set to: "@Global Aramika,@Aramika,@Global Aramikini,@Aramikini,Krecik"
(just testing out if everything works with groups and single user names etc.)
In the "Access Control List Management", the administrators (super-users) can set permissions for all (existing or non-existing) groups and members for each page and namespace. But in the Dropdown menu, only those groups and members are visibile which have already been assigned in some rules.
To set access rules for some other members or groups that are not yet listed in the dropdown, one has to select "Group" or "User" in the dropdown, and type in the username or group name exactly as it is in the SMF database. (And I don't know if one has to type '@' here before a group name as well, if one has already selected "Group" in the dropdown.)