4 days ago I had a pap smear there is still a small amount of bleeding (like heavy spotting) & mild cramps. Do I need to notify my doctor?

Not at this time. Now after a pap smear it is ok to experience light spotting. Also you may also be very close to starting you menstrual cycle, so i would recommend taking some over the counter medications such as tylenol (acetaminophen) or Ibuprofen and if your problems continue for over 1 week then contact your doctor.
Yes. What you described is not normal, you should consult your doctor and ask for the results of pap at the same time.
It might be wise. This could be a result of the smear, or some other process, like a possible cervical lesion, an endometrial issue/lesion, or another issue such as abnormality in the outflow tract or heavy period. It would be smart to tell your doctor to check for the cause since this did happen after a pap.