Adding a light to an existing switch
The black and white from the fuse panel is the constant power feeding two circuits: The bath light and the hall light. I take it the single pole light switch was used to control the old ceiling fixture. The two wires going to the hallway light need to be attached white to black from the fuse panel. That is one complete circuit.

CEILING FIXTURE: The two wires going to the light switch should both be considered "hot". Attach the switch black wire to the black wire from the fuse panel and the switch white wire to the black wire of your old ceiling fixture.  Attach the white wire of the old ceiling fixture to the fuse panel white wire. That's a complete circuit.

NEW FIXTURE: The switch can also be used to control the new fixture. Attach the black wire to the black wire on the old ceiling fixture. This will supply power to the new fixture when the switch is activated. Attach the white wire to the panel white wire.

In the end, the panel white wire will have three wires connected to it (all neutrals tied together). The fuse panel black wire will only have two wires connected to it because the switch will feed power to the ceiling and the new fixture at the same time.