Cannot get mailings to work
So you have two issues, that are probably not directly connected:

1) mail() working only when 'Save &amp; Send Test Email'
it uses a different sender (the default site email, as opposed at the one defined as the bounce mailbox)

They are various reasons so the later could fail, the most common ones are that you didn't configure properly the bounce mailbox or that your mail server prevents you to "impersonate" the bounce mailbox (eg if you use a gmail account for the bounce)

The documentation on how to configure is usually helpful, but if you can't walk through the steps, could you create a new question?

2) no smtp connection
It depends on how your server is configured, check with your host provider what is your smtp server, if it on the same box as your webserver, if it accepts local connections, or if it needs authentication.

if you really have the same error message when you put localhost, try 127.0.0.1, if it works, you might have another problem (wrongly configured dns on the server), because localhost must be seen as a valid address (ie. I was expecting a different error message)

Lastly, what hosting provider are you using? if you went for a "low cost" option (ie. less than 5$/month) you often have providers that actively prevents you to send mass emails and you will spend way more struggling with your server than the cost of switching to a more mass mailing friendly.