1.
You must use external smtp server, like external postfix / exim or Ironport.
All mail must be sent via external smtp server. Zimbra will be only pop/imap server and webmail.
Sample:
WEBMAIL: Zimbra can send all messages (to internal and external users) via external smtp, but only if you use ZImbra webclient.
SMTP: Therefore you must create an external smtp server (for smtp connection from internal users) and route all internal mail to your Zimbra server. External mail (non local domain) must be routed to the outside servers.- Internal users need to send all messages via external smtp server.
2.
Probably, there is the possibility of configuring master.cnf (Zimbra postfix) to send all internal and external messages to outside server (non local delivery option).
You can also read this post:
Integration of zimbra server with ironport