Both my wife and I have the same issue on our BlackBerry Key2 LE phones.
However, we use Thunderbird on our laptops and we are experiencing the same thing with authentication issues.
What we have found is to ignore the authentication messages as the emails eventually com through. Sending emails will sometimes show pending, but eventually go through.
I logged in to Outlook.com and it shows it is connecting both from Thunderbird and my BlackBerry Key2 LE.
I hope it gets fixed soon on Microsoft's end. I have always liked the tight integration of the emails, calendar and contacts so I can save it once and access it all from my other devices.