Hi Jerry, welcome to the forum.
You've asked several questions:
Your car won't be travelling at the speed of light or faster. Special relativity guarantees that. Because the situation is not possible physically we can't say what would happen with your headlights, but at that speed, you'd better hope nothing is in front of you.
If I am in my car traveling at or just above the speed of light and turn on my headlights, will they even make a difference?
You should try it and see. The sound waves add to the sonic shock front going forward, but are audible behind the horn.
driving my car at the speed of sound and honk the horn, what happens?
The sound would be higher frequency, and the light would be bluer.
if I get hit with a basball thrown from a moving vehicle, it will have a stronger impact becase it is traveling at the base speed of the platform + whatever speed it gained from throwing. Same true for slight and sound?
Forming opinions as we speak