Consider the case of the car starting at rest and accelerating forward. A. Since the air inside the car is not leaking out, it must also accelerate forward. What object exerts the force that is responsible for accelerating the air forward? (I. e. the earth, the air outside the car, the car windows, the balloon, etc.)

The force originates from the tires. Tires accelerate the car. The car interior in turn accelerates the air inside the car by providing a pushing force. Thus it is the car read windows, seats and side windows that push the air forward causing it to accelerate.

Explanation:

The air inside the car is being forced forward by the car interior. This includes the rear windows, seats, side windows etc.

This accelerating force originates from the tires, and makes the car interior accelerate with the car. The air inside (since it has no direct connection to the tires) is then pushed forward by the windows, seats etc.