Re: If I was on a spaceship going the speed of light...

This is very much the sort of thing that makes no sense to use because we have no experience with frames of reference which move at substantial fractions of lightspeed. A frame of reference is usually defined as a set of objects-plus-surroundings such that all portions are moving at the same velocity. The thing to realize is that you can't tell, from looking at your own frame of reference, whether you are moving or not! For example, if you were on a moving train and dropped a ball, you would see it move straight down to the floor. Someone outside the train, and at rest with respect to the train, would see the ball move forward as well as down.

Now a basic principle (I am not certain whether it is a premise or an early conclusion) of Special Relativity is that the velocity of light always appears the same in any frame of reference, even when someone in that frame is looking at light belonging to another frame of reference!!

Therefore, if you were in a spaceship moving at the speed of light and you ran from aft to fore, you would not appear to yourself to be moving faster than lightspeed. However, neither would you appear to be moving faster than light to someone at rest with respect to your spaceship! The consequence of this is that, to someone at rest with respect to your spaceship, time would not appear to pass for you; you would not appear to move inside the ship!

This applies to the headlights. To you, the light from the headlights would appear to move at the speed of light; but to someone at rest with respect to you, light from the headlights would be moving at the same velocity as the ship.

I suggest you look at the page I linked above. There's a lot of math on it, but also a lot of examples and some non-mathematical discussion of things relating to your question. Special Relativity is a lot of fun! Enjoy!