in reply to Re^2: Authentication Required
in thread Authentication Required
Could be there is nothing weird about that. Most SMTP servers are configured to accept mail to the local domain from anywhere and to send mail only from the local domain. This prevents some unauthorised machine (eg outside your local network) from using your mail server to spam mail to the world in general.
If your "From" address is somewhere inside your network and your "To" address is outside then the mail server should refuse to accept mail to the "To" address without authentication, while it may be happy to accept any message to the "From" address since that is a local delivery.