why does the differential make noise?
Low on fluid, gears and or bearings are shot.
I see in the records, "XX iffylube" changed the diff.fluid. Maybe they didn't use the recommended BMW spec. I should change it out to be sure....
I would take it to a good REPUTABLE European mechanic and have it looked at before you do anything or before you do anymore damage. That's my two cents worth.
Looking for a Used Z3 in your area?
CarGurus has 309 nationwide Z3 listings starting at $1,998.
Search BMW Z3 Questions
BMW Z3 Experts