Does light have initial velocity? You are standing still in a vacuum, and you throw a ball that moves 10 m/s away from you.  Now you start moving in one direction at 5 m/s, and throw the ball in the other direction, away from the direction you are moving.  The ball, relative to you, is going 10 m/s, but relative to an unmoving body, it is traveling 5 m/s.
My question is: is this same concept applied to light?  If a light source is traveling away from you at a speed greater than that of light, would you be unable to see it?  Or would light just keep going the same speed relative to an unmoving body?
 A: Special relativity deals with high velocities.
In special relativity, the relative speed of light is constant it always moves at $c$. Nothing can move faster than the speed of light relative to you. 
Also velocities are not additive in special relativity.
A: 
If a light source is traveling away from you at a speed greater than that of light, would you be unable to see it?

You'd be unable to see it because it would not exist. Speed of light's a limit. A light source moving away from you faster than that doesn't even make sense.
If it were moving away from you at the speed of light (well, really really close to it) then you would be unable to see the light that arrived from it because it would be red-shifted down below human vision.

Or would light just keep going the same speed relative to an unmoving body?

If there's a detector fixed to the light source, one on your planet, and one on a craft moving towards that light source at half the speed of light, the photon would pass through ALL THREE detectors at the speed of light, even though they are moving, respectively, at 0, 0.5, and almost-1 $c$ away from the light source.
But the three of them would not be able to agree on what time it was.
