The problem seems to be is you're trying to use a public DNS server when your Zimbra server is on a private IP behind a NAT device(?). Do you have a local DNS server installed? I've already pointed out a couple of errors in your DNS setup, they need changing and, as far as I can see, you haven't followed the 'How To Forge' instructions on setting up a Zimbra server. Now, again, do you have a local DNS server installed?
I do not have a local DNS installed. I tried installing one and everything quit working. I started over with a fresh install. Any recommenced reading on correctly setting up a DNS would be appreciated. This is all new to me and I really appreciate any and all help given.