The ports question would depend what you want to expose to the outside world, there's a list in the wiki
here. For instance, I only use https for the web UI (443), an IMAP client (993) and an extra submissions port (587) plus port 25. That should be all you need to use.
For the DNS you need to be careful what you specify, the zone you want is the domain name fairhavenchurch.org and not mail.fairhavenchurch.org The mail.fairhavenchurch.org is the FQDN (Fully Qualified Domain Name) of the server which consists of the server name (mail) and the domain name (fairhavenchurch.org), the distinction is important. When I first set-up Zimbra on my server I used the
DNS in a Nutshell thread (specifically post 2 in there) to configure BIND as I wanted to use that DNS server for external resolution for my LAN machines.
Does that cover what you need to get started?