Hi @Maira
Once you begin your Ausbildung, you may be entitled to financial benefits visa BAFöG and/or asylum seekers’ benefits from the Sozialamt. You should apply for BAFöG. Depending on how much you get, you may in addition receive additional financial support from the Sozialamt.
The 150€ bonus does not apply to those doing an Ausbildung. It is only for people who are in receipt of benefits (Bürgergeld) from the Jobcenter and who are doing a Weiterbildung (i.e. like a further training course, different to an Ausbildung).
If your husband needs financial support, as a recognised refugee he is entitled to Bürgergeld from the Jobcenter. The Jobcenter will also assist him in finding work or maybe doing such a Weiterbildung as mentioned. There are often specific projects in each part of Germany to help refugees with career orientation and finding work.
Your Steuerklasse will be 1 unless you have your marriage recognised in Germany.
Based on your description of your situation, I do not know of any residence permit which would be available to you. The most likely one I can think of is paragraph 19d Aufenthaltsgesetz as your university degree has been recognised. However, for paragraph 19d you have to have been working the past two years in an area related to your qualification.
Best,
Éanna