Q: When I sign up a customer, I get the following error:

Error - DNS zone already taken;
Error - Domain is already taken;
I can't find such existing domain (zone) with the Search utility and in the Awaiting Moderation list.

A: Back up your database first, then stop your control panel.
Next, connect to your system database:
su -l cpanel -c 'psql hsphere'
Then run queries against it to find out if the domain (zone) can be deleted.

You may find it helpful to write out the results of your queries, as you will need them on further steps.