Thank you IgorG, I will apply this in the next week ... I hope this will solve our issue.
the issue is very stupid: the hosting provider has installed Plesk but he have forgot to open the needed Ports. Her support had 2 months to find out, that they have not open the needed ports. Then we have open some ports and then it was possible to host domains with the name server of the registrar (after the needed changes in the registrars name server). Before this we had (at the same provider an other account who has worked fine wit our own Name servers. After we have changed to a new similar account, nothing would work with the old settings. Only after we have open some ports we can host domains and e-mail accounts with the name server of the registrar.
The support of the hosting company is very stupid ... they state, that our own name server must be on her host. But the reality is, that our own name server is a "Switch" under the control of the register/registrar: this "Switch" is a sub "Switch" of the register name server, and he sent the whole domain to the host. Plesk on the host must then handle the DNS without any specific changes in our name server (No A Record, no settings for the email). This has worked perfect on the old account, but the new account was not set up properly, and I think this issue is due to a closed port.
When we will install a domain, then PLESK seek for the name server of the domain and will install correctly the domain with our own name server. This is the best way to handle multiple domains without these stupid changes of the A-Record (and other settings) in the Registrars name server. The only thing to do is to create an own name server in the account of the Registrar and to give him the target IP (= the IP of the hosting). When PLESK is correctly installed then PLESK finds the name server and install the domain without any problems.
I open now all the ports listed in your list and hope this will resolve our problem ... if not I hope you will help me again.
Thanks,
brainstuff