Answer:
a. Diane may search the passenger compartment of the car and any place else in the car, including the trunk, without Tim's consent.
Explanation:
Tim's car is stopped for traffic offense, and that the police officer holds a legal right to stop the car in that case.
Further while in the conversation with Tim, if she notices that there is an evidence of drugs, and that are just not only the medicine, but heavy drugs which are not be consumed as a medicine but involves different purpose, she has a right to investigate thoroughly.
In the given instance also Diane can further search in the car wherever she wants, as she has an evidence that the car has some drugs.
For this she do not need to take any permission from the car owner that is Tim.