Hey,
in the Customers is this note:
Everyone with an account on this Jira instance is a customer.
Every User I have in the project is listed there beside one user. His role is just 'administrator'.
- Why is this guy missing in the customer list?
- Why is it possible for this guy to raise requests?
Thanks a lot for helping understanding this! 
In addition:
When I click on the Customer Permissions there is this option selected:
Customers who have an account on this Jira site
- What is the 'Jira site'? Is this the 'Jira instance'?