Officer  Smith is on routine night time patrol when he notices the vehicle in  front of him appears to have a broken taillight which appears to be  covered with colored tape. He directs the driver to pull the car to the  side of the road. The car is an older model gold Pontiac and as Officer  Smith walks to the driver-side of the vehicle, he remembers that a car  fitting this general description was the suspected car in a recent road  side killing of a fellow police officer. Wanting to make sure that he is  safe, he asks the female driver to step out of her vehicle for a brief  pat-down for weapons. He pats her down and finding no weapons, Officer  Smith asks the driver to have a seat back inside her vehicle. He then  asks her for her driver's license and registration. Instead of providing  her driver's license and registration, the driver speeds away resulting  in a high speed chase. The chase ends when the fleeing car hits a  telephone pole and crashes. Concerned that the car may ignite in flames  from a leaking gas tank, Officer Smith removes the unconscious woman to a  safe distance from the vehicle. He returns to the vehicle to locate her  purse for identification. As he enters the vehicle, he notices the  glove compartment has popped open and that underneath some documents is a  gun which he retrieves. He also retrieves the driver's purse from the  floor on the passenger side of the vehicle. He opens the purse to get  the woman's identification and finds what appears to be a baggie of  marijuana. It is later determined that this vehicle was not the car  involved in the shooting death of the fellow officer. It is also later  determined that the taillight was not broken.
 1. Did Officer Smith have reasonable suspicion to make the initial stop of this vehicle?
 2. Was the "pat-down" of the driver legal?
 3. Did exigent circumstances exist for Officer Smith to give chase to this vehicle?
 4. Was the gun in "plain view" and legally obtained?