Here are what I found,
1) the there is a custom field group "Zusatzleitungen kostenpflichtig"
Dashboard-> Toolset-> Post Fields, find and edit field group "Zusatzleitungen kostenpflichtig", there are three custom checkboxes fields in it:
a) Premiuminserat + 15 €/mtl p. Inserat
b) Escort des Monats + 25 €/mtl p. Inserat
c) High Class Escort Inserat +10 €/mtl p. Inserat
All of them have only one option in each checkboxes field, that cause the problem,
The checkboxes field work for multiple choices field, in your case, I suggest you try these:
1) create custom checkbox fields to replace them
2) Edit the CRED form, put above checkbox fields into form content, and test again.
I have now created new custom check boxes with the same settings. However, the problem persists
It works fine in my localhost with your database dump file, please check these:
1) You are using custom checkbox fields instead of checkboxes field.
2) If the problem persists, please provide a test site with same problem, and fill below private detail box with login details, I need a live website to test and debug, thanks