Yes, tried to suggest that about the link found for Debian. In your IP Tables config, you don't show port 25 (the smtp port) as being liberally allowed as the other ports ... last statement there denies all that are not listed. Think that's why some messages not being received. Moodle was attempting to send, but blocked by the local MTA/IP Tables.
Consider installing Webmin on your server. Perl based so even if apache/mysql/moodle down, one has access. Has lots of tools to help admin a Linux server (including exim4, I think) - even helps one find things is not known ... like the mail logs, etc.. and backup DB. etc..
'spirit of sharing', Ken