You need a school transfer application (change of school) if your child is not supposed to attend the primary school assigned to your residential area (catchment area school), but a different primary school.
The central authority for asylum procedures in Germany. The BAMF (Federal Office for Migration and Refugees) has offices in all federal states, which are called branch offices ("Außenstelle").
If you are doing a dual apprenticeship in Berlin, you will often go to an Oberstufenzentrum (OSZ) vocational school (upper secondary vocational center).