It is usually a good idea to have 'Must send from known domain' set to True/Yes. Other than that the settings are pretty normal and look OK.
It sounds as though the mail arriving is addressed to a domain email address. i.e. if the site is https://www.mydomain.com then at an address like [email protected] - a local address, or possibly local to the ISP hosting environment.
Which means that mail delivery from the site works fine as far as the local mail server, but that the rest of the world wants nothing to do with dodgy and suspicious looking spam. i.e. the domain mail setup or hosting config is incomplete.
If the mail is bounced, it probably has nowhere to go, as no postmaster or bounce mailboxes have been defined, so it falls into a black hole.
Possible reasons include - mail server is blacklisted, mail is being sent as apache user 'nobody', hosting co mail server is not listed in the MX records of the domain, no SPF record for the domain, no return path, no reverse DNS etc etc etc.
http://www.dnsstuff.com
and a DNS report is often a good place to start, to verify the basic domain mail setup.