Hi Christian,
Thanks for providing such detailed information.
As you said, the issue may not be related to the Autodiscover DNS record since your Outlook 2010 and Outlook 2013 can work fine. And the SSL certificate warning is considered an expected behavior when performing an Autodiscover RCA (Remote Connectivity Analyzer) test.
Given the current situation, please try your account with another Mac which has Outlook for Mac 2011 (or the newly released Outlook for Mac 15.6) installed. If the issue doesn’t occur to the other Mac, we can determine the root cause of it is about the Outlook client.
And if it does occur to the other Mac, I suggest you perform an RCA test for Exchange Web Services (EWS) since the EWS also plays a part when connecting Outlook for Mac client to the Exchange Online services.
If there’s any error (not warning) reported in the test result, please send us the entire test result (click the Expand All button) through a private message. I’ve sent you one with the subject RCA Test Result, and you’ll see it by clicking Private message under your details in the upper-right corner of the forum page.
Thanks for your time and efforts on this issue!
Best Regards,
Allen