To conclude: The server is back online. Enjoy your evening/night. ;)
When it comes to divisions, we will have to restart the servers to fully fix the issue. This is going to happen at the usual time in the early morning (3:00-4:00 UTC).
In the meantime, if a division invite is not being send, simply recall the invite and try again. This should fix it. Thanks to @muffmunchingmegamonster for discovering this.