Hi There,
The second error (external test) is normal (and expected) if your server is setup for SMTP authentication, as it should. Let's look at the first error, though.
If you go to a command prompt and type
and
What are the results in the command window?
If you go into server options look for a place to set specific DNS servers; I am not in front of my server and cannot recall where. However, you can set them specifically to 8.8.8.8 and 8.8.4.4, and restart the server, that should fix your lookup issues.
Joe