Dear Karin Alex,
Welcome back to the Wefugees Community and thank you for reaching out to us again.
The website of the Federal Foreign Office (Auswärtiges Amt) is giving information on marriages which took place outside of Germany.
Also "Handbook Germany" is providing some very useful tipps and information: "If you marry abroad, you need to have your marriage officially registered in Germany as well. To do so, you must submit an application for a certificate of marriage to the relevant Civil Registry Office. You will also need to present your marriage certificate and, if necessary, a so-called "apostille". The apostille is an official document confirming the authenticity of the marriage certificate. All these documents must have been translated by a certified translator."
So the first step will be to contact your local registry office (Standesamt) - I am sure they can give you all the details on the required documents etc.
As long as your marriage is not registered, the tax office is listing you as single and you can not benefit from potential benefits for married people. I did not understand exactly what you wanted to ask on the asylum procedure. Maybe you can get back to us again and explain a bit more.
I hope this helps and all the best,