Your 'internal' can be the same or different to your real domain name but I 'd recommend you keep it the same for clarity.
Your hosts file only needs to contain the following:
You would normally have an extry in your /etc/resolv.conf like this:
127.0.0.1 localhost.localdomain.com localhost
192.168.1.110 mail.mydomain.com mail
The set-up in the wiki that I've given you assumes that the Split DNS server resides on your Zimbra server - if you used another DNS server then change that IP.
You also seem to be getting the correct response from your DNS records but the 'host `hostname`' command is returning the wrong IP - it should return the LAN IP of your Zimbra server. Make the changes I've mentioned the try the host command again.