Apr 3 21:44:54 mail01 postfix/smtp: connect to 127.0.0.1[127.0.0.1]:10024: Connection refused
First of all you should try to manually start the service
[root@mail01 conf]$ su zimbra -
[zimbra@mail01 conf]$ zmamavisdctl start
Starting amavisd... The value of variable $myhostname is "mail01", but should have been
a fully qualified domain name; perhaps uname(3) did not provide such.
You must explicitly assign a FQDN of this host to variable $myhostname
in amavisd.conf, or fix what uname(3) provides as a host's network name!
If you get this error you made a mistake like I did. I did gave the fqdn while setting up the server. You can fix this by executing
/opt/zimbra/libexec/zmsetservername -n mail01.demo
Then do an exit to get you back to the root shell and reboot