We live in a duplex which was built as such. I am sure that the wiring has been replaced at some point due to all of the new fixtures and the age of the building.

When my neighbor's bathroom fan turns off (and possibly his bathroom hot lamps too), I hear a very clear "click" over my speaker system.

Realizing that these two systems are supposed to be completely separate, should that kind of interference happen when they use their devices? It almost seems that somehow their bathroom electrical was wired into ours.

Our electrical bill seems high, but is of no use at the moment since we have just moved into the place. We can't compare it with any control bill for measuring purposes.

Any thoughts on this? Thanks for your time!

Does each unit have its own breaker panel?

There is probably a spark from the switch and as such causes static. Is your speaker on an abuting wall?