Move or remove a downspout inside brick wall
I suppose you'd call a plumber. You must determine if this is connected to the sanitary sewer. Also this opening should be capped with a proper cleanout fitting with a cap that would prevent sewage from pouring out, but would be removable for inspection or clearing a blockage. The plumber could run a camera down this and see where it goes.

AFIK rain water is not supposed to be directed into the sanitary sewer. Does DC allow this? It may be they accept it under grandfathering . . . or not.