Sorry you've had all this trouble. You might try reading some of the documentation here:
http://www.zimbra.com/downloads/index.php
It talks about our architecture and the dependencies we use. It would have explained that we ship all our dependencies (MySQL, Tomcat, OpenLDAP, etc).
They are ways to make Zimbra play nice with existing http servers and databases. It doesn't come out in the installer so you've got to make some changes but many folks here on the forums have made it work.