thank you for sharing your question with the Wefugees Community!
Unfortunately if you are still in the asylum procedure with a "Aufenthaltsgestattung" you are not eligible for BAFÖG right now. But you can become eligible if your procedure ends with a positive decision or if you receive a "Duldung" and your all-together time in Germany is more than 15 months. I assume that is also what @helios meant.
Yes, you are officially allowed to study in Germany. But if you are eligible to do your masters degree in Germany depends mostly on the conditions of the university you are applying at. But if you already looked into the different universities and courses and found something that fits for you I am sure that you are aware of it.
Regarding your question about moving to another city:
I assume you are having a restriction to live in a certain area in Germany - in your case in Frankfurt - right? This would be a so called Wohnsitzauflage. If this is the case, it could be possible for you to move to another city if you don´t need financial support from the state anymore. With a scholarship which would cover all the expenses of your studies as well as you living expenses, the chances therefore could be good that you would be allowed to move. But since I am not an expert on this topic and I don´t know all the details about your case, I can´t tell you for sure.
It would be probably best, if you talk to your local immigration office (Ausländerbehörde) about it and ask them what kind of documents and proof they need from you. If they reject your request right away or don´t want to cooperate I would probably recommend you to look for a local counseling centre/office close to you that is maybe even specialised in work/study issues. I will link you a Website where you can look for such independent and free counseling options in your region:
I hope this answer was helpul for you! Please don´t hesitate getting back to the the Wefugee Community if you have further questions!
All the best,
Note: Please keep in mind that we can´t provide qualified legal advice via the internet and that any information given can´t replace such legal advice.