Ok, First I applied the patches for the wrong octal-format (leading zeros) and fixed the permissions to allow entering a VAT-ID.
Also, I put in a VAT tax-rule for 19% (germany) and added the condition that the state must be inside EU.
Now, when the customer enters a VAT-ID and if he resides inside the EU the system still shows VAT on the checkout.
I think I need a condition to check if the VAT-ID has been entered and then remove the VAT. But how?!
Thanks for any help or comments.