Q. 4:
It is true that wider tires commonly have better traction. The main reason why this is so does not relate to contact area, however, but to composition. Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. Softer tires have a larger coefficient of friction, therefore better traction. A narrow, soft tire would not be strong enough, nor would it last very long.