Welcome to the Wefugees community and thank you for sharing your situation!
If she has applied for asylum in Germany, it is correct that you two can get married in Germany. You just need to make sure that you fulfill the requirements and that the marriage will be recognized in Denmark, if you plan on living there. Here is some more information on How to marry in Germany from the Wefugees Blog: Click here.
[Please note that Dublin III might apply in her case, if you say she had a visa for Denmark before. Germany might see that as a reason to decline her asylum claim, as they recognize Denmark as the responsible country for her claim.]
To answer your first question: she doesn't automatically receive a residence permit when you get married, but, by marrying a EU-citizen, she has the right to apply for it even while the asylum proceedings are still running.
Getting married and applying for family reunion are two different processes. As for applying for family reunification - I've had a look and there is, indeed, a 24-year age limit:
"You and your spouse/partner normally need to be at least 24 years old in order for you to qualify for family reunification. This is known as the 24-year requirement.
You may submit your application for family reunification when the younger spouse/partner is 23 years and 6 months.
Exceptions from the requirement
The Immigration Service can suspend the 24-year requirement in special situations, such as if you, the applicant’s spouse/partner in Denmark:
You as a EU-citizen are able to travel to Germany and get married to your girlfriend, the age limit to do so is 18+ (just make sure to bring all the necessary documents). However, if you want to apply for family reunion in Denmark, to live there as a married couple with a residence permit, it looks like the age can be a problem. You may have to wait until your wife has reached 23 years and 6 months at least, before you will be able to apply.
Here is more information on Danish family reunion regulations.
It might be best to talk to a refugee support service in your area about your options. Another way would be talking to the Danish immigration service about family reunion and what your options are.
Here's a list of places offering free legal aid for refugees: http://www.refugeelegalaidinformation.org/denmark-pro-bono-directory
And the contact details of the Danish Immigration Service: https://www.nyidanmark.dk/en-GB/Contact-us/Contact-the-Danish-Immigration-Service/Call-us
Let us know if you have any more questions or need further assistance.
All the best,