Hello @Krmysl and welcome to our community!
If you can provide all the required documents you can get married in Germany even if you are still in the asylum process (see this thread for further information: https://www.wefugees.de/k/questions/1997
But your fiancé will not be granted asylum on the basis of the explanation that you suggested. You can only get a refugee status if you can prove that the situation in your home country is unbearable and that you need shelter by another state (for example due to persecution, danger of life or other types of violence and/or life-threatening circumstances).
First you need to talk to your competent registry office (“Standesamt”) and apply for an appointment to get married. After that your fiancé can apply for a visa to get married (“Visum zur Eheschließung”). She will need to hand in the following documents/papers at the German embassy (or another competent diplomatic representation):
- a written confirmation of the appointment at Standesamt
- proof that she has basic German knowledge (A1 level)
- a copy of your residence permit and passport
- they might ask for other documents as well
The German agency abroad will send this visa application to Ausländerbehörde and they will invite you to an appointment. There you need to bring a non-marriage certificate (“Ledigkeitsbescheinigung”) and (if you’ve been married before) a divorce decree (“Scheidungsurteil”). Again, they might ask for additional documents.
Ausländerbehörde will check the whole application and tell the German diplomatic representation about it. The agency abroad will then decide on the visa application.
At least that’s the procedure in Berlin - it might vary from federal state to federal state. Source (German language): https://www.berlin.de/labo/willkommen-in-berlin/einreise/visumsverfahren/artikel.283140.php
Keep in mind that technically speaking this is not family reunion. As you already pointed out family reunion doesn’t work that way because you are not family members yet.
Yes, you can travel to Denmark using the blue passport. I’m not familiar with Danish marriage law, but it seems to be a little bit less bureaucratic than in Germany. It’s probably best to get in contact with the competent registry office that you want to get married at and ask them what requirements they have and what documents they need exactly.
After the marriage your wife can apply for a visa for family reunion (“Visum zur Familienzusammenführung”) at the German embassy and go through the regular procedure.
Source (German language): https://www.buemlein.com/service/ehegattennachzug-einreise-und-aufenthaltsrecht-wegen-ehe/#Heirat