thank you for your question in the platform and congrats to your marriage.
As for the registration process of Danish marriage papers please follow the Link as it has been outlined in the past:
In regards of the residence permit:
You and your wife have to address the Ausländerbehörde in order to swich from the Tourist Visa to a Aufenthaltserlaubnis, however they might ask you to go back to your home country and apply there at the German Embassy for a family reunion visa. But there are exceptions and it would be best if you get a lawyer who can help you with the process at the Ausländerbehörde/Landratsamt.
I hope we could assist you with your questions, if you have further ones please feel free to address them to the community.