Zimbra doesn't use port 7071 for https (that's just the admin interface) it uses port 443 which is the normal browser https port.
I assume you have your web server on another machine other than your Zimbra server?
Please refer me to a wiki as I have not seen any entries to address what needs to change in DNS for multiple domains. The only article I have seen suggests all one needs to do is add domains under configuration/domains logged in as admin. I have duplicated dns settings in regards to MX records from 3coffice.com, whobig.com and fnamail.com. As shown at Untitled Document
Please help or refer me to a helpful source. Thank you