It seems there's two issues here -
1. The longer term one of Mail not recognising a msn.com domain name, which my previous reply fixed (at least for me) 2. The other problem is the syncing, which is a current issue at Microsoft:
https://portal.office.com/servicestatus
Title: Can't access or synchronize Outlook.com email
User Impact: Users may be unable to access or synchronize their Outlook.com accounts while using applications or mobile devices.
More info: While we're focused on remediation, users may be able to access the service by logging in to their Outlook.com accounts with a web browser as an alternative method.
Current status: We've identified the cause of the issue and we're preparing a fix to be deployed to the affected infrastructure.
Start time: Thursday, November 17, 2016, at 12:00 AM UTC
Next update by: Wednesday, November 23, 2016, at 2:00 AM UTC