1) No. It does not matter which domain you use for the mx as long as it exists as dns A-Record which points to your server.
One thought, have you added the dot at the end of all domains? This is nescessary to tell the nameserv er that the domain is a absolute and not relative domain. example:
MX (2nd domain.tld.) (mail.domain.tld.) 10
and not just:
MX (2nd domain.tld) (mail.domain.tld) 10