I register my domain at a registrar and add my NS there. On my server I add the next DNS records: If I change the NS records on my server will it work or do I need to change them at the registrar?
Yes at register you must define both ns1 and ns2 for your domain. Also you will need two A records in ispconfig pointing to ns1 ans ns2. Cheers
I get these result via network-tools.com: Do I need to change the SOA as well? If I don't understand how should me customers? ;-) Is there not an easy way to get this done?
The dns system is a bit complicated and requires some knowledge if you want to run your own dns server. Each domain name that you want to use for whatever has to exist in dns. So if ns1.server.com and ns2.server.com are the nameservers of a domain, then you have to ensure that both exists at dns a-records in the zone server.com and they they point to your primary and secondary dns server. If you like to dig deeper into dns, then you might want to read trough the traditional dns tutorial that explains all the basics of the dns system setup.