external: domain of sender address does not exist talking to my server
 

I'm new; I had mail issue that I've only been able to research 1/2 the solution... help very much appreciated!

Cobalt Linux release 6.0

I can send mail to internal users, I can send mail to domains outside my server, sendmail works from my contact webpage, but I cannot receive email from outside the server.

History of issue:
warning message rec'd while using email that
Mailbox vulnerable - directory /var/spool/mail must have 1777 protection

I looked up the permissions, seemed reasonable, so I changed. Then no email allowed.

Changed back using
chmod 775 /var/spool/mail
...but only user-to-user email worked and no sendmail from webserver

so research and found I should
chmod 775 /var/spool/mail (and)
chown root.mail /var/spool/mail
...user-to-user works, sendmail works

...but email from external server is rejected:
-----
Unable to deliver message to: <user@mydomain.com>
Delivery failed for the following reason:
501 5.1.8 <user@hotmail.com>... Domain of sender address
user@hotmail.com does not exist, while talking to ip_of_my_server

This has been a permanent failure. No further delivery attempts will be made.
------
It looks as if my server cannot resolve domains, but /etc/resolv.conf looks like:
search mydomain.net
nameserver correct_ip_address1
nameserver correct_ip_address2

Thanks in advance for the help.

:study:Is this just kinda difficult, and people are still researching?:study: