1990 521i oriiginal fuel pump -- normal whirling

That is normal until the engine starts. It builds up pressure and shuts off until the pressure drops at the injector when they start working when you crank the engine.

Fuel pump in the tank makes a high pitch sound which is normal. Turn your key in the ignition, but don't start, you should hear the high pitch sound with the pump priming the system. You will still hear it when started, it's annoying but normal. Different brands are quieter than other, I just replaced mine with a Delphi brand fuel pump which is a tad quieter than AC Delco stock pump.

This is normal during colder weather .

This problem sounds intermittent. To ensure fuel pump is working, open fuel door and have an assistant turn on ignition switch to on position (NOT START POSITION) and listen for pump to make a whirling sound. Do this a few times after shutting switch off. Also, If you dont here pump whirling, you can spray starting fluid into air cleaner. If it starts , then its the pump

Fuel Pump and fuel filter change sounds to be what the Dr ordered also change the fuel pressure regulator all at the same time. You will be 100%

sounds like its turning over but not firring.
I had this problem with my 1992 525i and it was the fuse for the fuel pump. there was no fuel pressure. i have another one and it had the same problem but it was the fuel pressure regulator had failed. this is situated on the fuel rail and has a vacume line attached to it. good luck.

open gas cap to make sure pump is working, listen for whirling sound, if not check fuse or fuel pump relay

check fuel pump open gas cap and turn on key to listen for whirling sound, if not check fuel pump relay, listen for clicking sound

firt check the fuel pressure with a gauge `or just listen in the fuel cap while someone turns the key on, i fyou hear a whirling sound is running, also check fuel pump relay and fuse.......

Sounds like fuel pump pressurizing the fuel system. They do that for 2-3 seconds and then it stops (for fuel injected vehicles).