How much current actually passes along household neutral?
On any individual circuit (lamp or 120V outlet) the current in the neutral in that circuit is equal to the current in the "hot" wire.

If you have equal loads between black and neutral, and between red and neutral, the "black" current and the "red" current will cancel in the neutral - there will be no current in the shared neutral wire.

Anything that only uses 240V (hot water heater?) will not connect to the neutral, and therefore will not cause any neutral current.

An electric stove will use 240 V for the heating elements, but also uses some 120 V for lights and a clock, so will require a neutral connection, and so will generate some neutral current.

The current in the neutral wire between your house and the power company's transformer will depend on how the loads in your house are balanced between the two "hot" wires.