Hi, Zimbra definitely needs a DNS Server as it requires an A- and an MX-record. Since you do not have a DNS domain yet (I presume), I would suggest installing a local DNS server (e.g. BIND) and then configure your own domain there.
After installing and configuring Bind (setup forwarders to your ISP's dns!), just edit the /etc/resolv.conf file and point it to 127.0.0.1 or your server's IP address.
Also, remove the lines in your /etc/hosts as they will only cause confusion and other errors later on !