Johnshead, your questions have a basic problem. You are confusing frame of reference. In relativity the frame of reference (in this case who is measureing the speed) makes all of the difference.
How would you know that this car is traveling at a speed very near the speed of light?
A possible answer is that you might see me traveling away from you at near the speed of light and conclude that I am stopped so you must be the one moving. But you could look at it another way, the car could be stopped and I could be the one moving away.
A car that is moving at near the speed of light in one frame of reference is stopped in another frame of reference. If you are in the car, the car would appear stopped to you and you would measure the light moving out of the backlight just as it does in any stopped car.