Answer
a. The momentum it loses is passed to the Earth
b. Static friction
Work Step by Step
(a)
Your car is in contact with the Earth (the road). It loses momentum as friction causes its speed to become zero. The momentum it loses is passed to the Earth, whose momentum increases.
(b)
Your car is in contact with the Earth (the road). When the wheels begin to rotate, they push against the road with a certain force. The road pushes back in the opposite direction with a force (static friction) of equal magnitude in the opposite direction. The earth loses momentum, the car gains it.