Crashes+noise from FP2 when plugged into car

Have you also tried the same setup with another phone or simple mp3 player?

2006 is 12 years back. If the car has any active filter components installed such as low/high-pass for the 12V charging socket, audio system or else the capacitors may be spend by this period. So maybe any connected device could show this effect.

Plug (attached to a cable) or socket??

Perform some more tests and different combinations to separate if caused by the car (which I rather tend to believe) or the phone itself: so to find out if aux plug or 12V output causes this

  1. With a different device too (should reveal if your individual FP2 problem)
  2. Test Audio noise (pause/playback) while USB charging and while on battery (charger issue or not/maybe 12V dc output related; noise being introduced by the aux plug
  3. Test internal phone speaker noise while pause/playback when USB charging and when on battery (aux plug / car HiFi system not involved).
  4. Perform all tests with engine started and also with engine cut-off

Take off the phones cover and carefully connect to the cars HiFi system again. Some users have audio connection issues (with the slim covers).
I am using Bluetooth earbuds, but since I have a slim cover replacement I know for sure about this design flaw.

Not sure if audio jack or headphones is the problem

FP2 audio jack has a 4-pin design (for using audio equipment with microphone & controls). Conventional audio jacks/plugs only have 3 pins. Properly plugged things usually work fine, but if the connection is not matching well no one can tell for sure how results will be.

Not me.

Feel free to get your 12V dc output checked professionally with a multimeter or even oscillograph. The battery in idle-state should always deliver >12 volts otherwise its not fully charged or beginning to die. With running engine (properly operating and charging generator assumed) dc output may go up to 13,5 volts.
Depending on quality your USB charger should not pass through any noise and keep its 5v dc output constant depending on how much load is actually connected.

Assure to keep it somewhere where it is save from overheating and able to emit heat caused by charging and running processes.

Did you replace with the same HP USB charger?

It looks like some homework to be done. Good luck.