OK, had change the server already with an full new installation of both Debian Wheezy and ISPConfig 3.
All domain are set on Registra Nameserver and not any DNS Zone inside of ISPConfig 3. SMTP (Send Mail) is set to the Relay of my ISP and that's working fine now. I tested with 5 different Domains from 3 Registra's and all went well till now.
To transfer the regular Domains to ISPConfig I'll have to that on Weekends, mainly at Sunday's, because of those 24h those domains maybe no visible on the Internet.
Thanks a lot to Till for his help to get everything up and running!