Was muss man bei einem Umzug alles beachten irgendwelche Anmeldungen oder Steuern oder so?

You need to re-register your residence and, if available, re-register your car (but you may retain your current license plate). You should also inform your banks and insurance companies.

With regard to the tax return, you can submit the normally further via elster.de and the rest with the tax to the new tax office will then take over the tax office. When you enter it on paper, you enter it at the new tax office and write your previous tax number at the old tax office into the corresponding line of the main form.