The bullet on the train depends entirely on frame of reference
To someone sitting on the train the bullet will whizz past them (or into them) at 2000km/h. Remember that any inertial (i.e. non accelerating) frame of reference is indistinguishable to any other one, and if all the windows on the train were blacked out and there was no horizontal rocking motion because in the future when trains travel at 2000km/h they will be able to build tracks that well too
then someone sat on the non-accelerating train would not be able to distinguish between their state of constant velocity and being stationary. I don't tihnk I have said this very clearly and concisely, but basically to someone sitting on the train the bullet would act just as it would if both shooter and observer were standing outside on the grassy field.
To somebody standing outside on the grassy field though the bullet would appear to stay in mid air while the rest of the train moved past it. (and they therefore would still see it whizz past the observer on the train but because of the observer's motion, not the bullet)
A more interesting variation on this question would be if someone fired the bullet out of the window in a direction back along the length of the train, or even forwards in the same direction as the train was travelling. Would the bullet ever leave the gun? 
As for speed of light question, where? Where?
Relativity is my pet hate of a physics subject though X(
tweehonderd graden, dat is waarom ze me mr. fahrenheit noemen, ik reis aan de snelheid van het licht, ik ga een supersonische man van u maken