I have had lots of problems since upgrading to the new 365 settings with sending mail from my Mac. I have a business 2Wire hub from BT. The settings are not the same as those installed using the widget downloaded from the BT website. The correct settings were put in remotely for me by the BT chat team and look like this:
Incoming mail pop.outlook.com
tick SSL using port 995
Outgoing mail smtp.outlook.com
tick Custom Port using 587
tick SSL
Passwork authentication - input full email address and password.
Sorry if this post is not very technical, but then neither am I. This appears to have sorted out my sending problems.