Hi - my apologies but I don't really understand German so I couldn't read the logic in your form. :)
Anyway, are you saying the my suggested method does not work? Hmm, looking at only the radio buttons in your form, I see that the field is named Accountaktion and that it has three options: Einrichten, Ändern and Deaktivieren. What I was suggesting was that you'd use value selected in the radio button as a condition in your data validation rules. For example, one condition can be if the Accountaktion = "Einrichten" and NameAntragsteller is blank, then display an error.
And I see you're already doing this for most of the fields in your form. You just need to add the same logic in your other fields that depend on the selected radio button's value.