Exim is trying to deliver the mail to a remote SMTP host and is failing. This is what the:
R=lookuphost T=remote_smtp defer (-44): SMTP error from remote mail server after RCPT TO:
lines mean. It queues these mails up for retry, and skips through the mailq to see if it should attempt to redeliver any of these mails. It won't attempt this straight away, a predetermined timeout has to be reached. This causes:
routing defer (-51): retry time not reached
Finally, when the max redelivery attempts is reached without success, it tries to deliver a mail to the postmaster (which by default is configured as root). However, the default exim configuration is to never deliver to root, so you get:
**User 0 set for local_delivery transport is on the never_users lis**t
There's two problems here:
Firstly: exim can't deliver to this particular SMTP server. Either the destination SMTP server is broken, or Exim cannot deliver to any SMTP servers. Does exim deliver mail to address on other domains? You can test this on the command line with:
/path/to/exim -v 'email@example.com'
message here
^D ( control D )
Secondly, you don't have a valid way for exim to report failures back to you. Configure your /etc/aliases file to make sure that the postmaster and other accounts are properly aliased to a real address.