Hi @Derek
I already answered your other similar question on this. As for the address issue, you have an apartment in Bremen so you register (Anmeldung) as living in Bremen and then send the confirmation (Meldebestätigung) to the immigration office.
I do not understand the second part of your question. You seem to be referring to different applications and processes for a work permit and a residency permit. There is only one application you make, with or without a lawyer. This is the application for a residence permit with the immigration office. As part of the procedure, the immigration office sends the job offer to the Agentur für Arbeit for approval. You are not involved in this. Once the application is approved, you are issued with a residency permit which includes the right to work.
Best,
Éanna