Exactly as I thought, you missed adding some records. The zone lacks A-Records for ns1 and ns2. Add the two A-Records and you will see that BIND will accept the zone.
Yes. That worked. Do I need to do the same with my other domains? The other domains work without the ns1 and ns2 A records. Should it still be done? Thank you for all the help till. Do not take any offence but at the moment the DNS system on ISPconfig is overly complicated. I would think that the "wizard" would be able to figure this one out.
No. You told BIND to use non-existing DNS servers for this zone and that's what BIND complained about. Not ISPConfig is complicated, the DNS system itself is as it's very powerful part of the internet infrastructure. The DNS system offers a lot of options and ISPConfig allows the admin to use the power of the DNS system. When you run a DNS server, then you should know how the DNS system works.
I propose an an idiot mode for those who have no idea what the internet is But I will post it as a suggestion in a different thread. Thank you again for all the help!