Hi @pschwarz,
I have to prefix my answer with the hint that at least in the past the Outlook app for android/ios did not directly talk to the server, but routed all connections to a man in the middle (which then obviously also has to know about your password). At least in my test connections from the app still showed a different ip, then the one my device actually has.
I have just tried this with a test user and for me everything works (can login, sync and send mails). there was an advanced settings screen during account could it be that the # snuck in there?
edit:
Funny how you dismiss the possibility that an update of the app could be the culprit 