I have a vague notion but I'm not clear on the difference between local domains and "relay domains"
I believe that local domains are "localhost" and any other aliases you set the server up to mean "self".
I believe "relay" domains are "everything else?" Like if a DNS has foobar.com point to this server, then foobar.com is a relay domain? I am not sure about this point.
In the exim setup file - (exim4.template.conf) What does it mean "fallback MX or mail gateway for domains" - what is fallback mx? Does it mean your server is like a DNS server of sorts?