welcome to our community!
If you need support with life situations related to your transsexuality you can get in contact with MILES:
You can go there on monday (2-5 pm) at Akazienstraße 3a, 10823 Berlin (no appointment required).
Concerning your question about work permission:
If you want to work while you are still on the process you have to ask the Ausländerbehörde for permission. In addition, you have to get a permission by Arbeitsagentur, but the Ausländerbehörde will do that for you - you don't have to apply for it by yourself.
The same applies if your process ends with a Duldung.
After four years of residence you don't need the permission by Arbeitsagentur anymore.
I hope this answer was helpful to you.
In addition, I will link @Malica . She might have further ideas where LGBT migrants can get support in Berlin.