The speed of light is invariant. No matter what velocity you or anyone else are moving at, you will all measure the speed of light to be the same. The frequency you measure will not agree, however.
As for your example:
Say we are in a rocket traveling at .6c. We have a proton gun and we fire a proton at .8c, relative to us. Relative to someone stationary outside the ship, what speed do you think they will see the proton traveling at?