If you have been married to someone and you want to get married in Germany again, you need to prove that your previous marriage has been divorced. So if your Aufenthaltsgestattung says “single” that shouldn’t turn into a problem when you want to get married again. But I can’t tell you in how far it might be an issue during your divorce file. The judge probably wants to know why it says so, even though you are legally married to someone.
Concerning your second question:
As I said, you need proof that your previous marriage is divorced. To do so, you can hand in your divorce decree along with the other required documents at Standesamt. You can find an overview about that in this thread of yours:
As Baris pointed out in the thread linked above, some documents need to be verified by the German embassy in your home country first. But I can’t tell you if this rule applies to you. May I ask where you are from? I can do some further research then.