thank you for your question and we are very sorry we could not get back to you any sooner, as I was on sick.leave and could not address the questions in time.
But as for your question:
it is right there are many Jobcenters in Berlin and depending where you will live in Berlin the one responsible for you is determined. Berlin is devided in districts(Bezirke) and according to your place the district differs that is responsible for all administrative questions.
Here is the overview:
As you are unemployed you might be eligible for WBS(Wohnberechtigungsschein) this allows you to get apartments that are supported/funded by the state:
I hope I could assist you- if you have further questions please do not hesitate to contact us.