English Translation
She is looking for her car keys.
Is using “od” here the norm? Wouldn’t using genitive only in samochodu be enough?
Yes, it is mandatory. If you skip it (kluczyków samochodu), it implies possession, meaning that these keys are owned by the car - like for example kluczyki Pauliny (Paulina’s keys) or buty Pawła (Pawel’s shoes).