Hi,
The admin notification email will work even in the starter edition.
The menu to configure emails is however only available in the Business edition, but the email is activated by default, like all the other emails.
Please check with your hosting company that the fact that the email has the same sender and receiver is not a problem. Also, filling the bounce email could result in problems on some email servers.
Otherwise, you should try to change the "Order creation notifications email address" option of the configuration. That might help avoid the such email server issues.