If your car could travel at the speed of light, would your headlights work? ~

Anything with mass can approach the speed of light, but will always fall short, even if only by one part in a billion.

A car going 99.9999999% of the speed of light will still have a working headlight, and in its inertial frame of reference, the light emitted in a vacuum, in all directions, will be the speed of light.

Hmmm thats a good question

Do you mean would they help?

No.