I am looking to transfer some websites with some roles (web, mail and databases) to a new server.
Are the DNS records automatically updated for the websites transferred? Does this include custom records?
If the domains nameservers are set to your enhance clusters DNS then yes they will.
If your domain is using 3rd party DNS then no, you need to update them manually.
Only the A record is updated. Custom record will not be updated. Why not give it a test, domain doesn’t need to be real or live.