As for beams, the answer is simple: light always travels at the speed of light in all reference frames. So even if you're moving at warp five and the other ship is moving at warp five, a beam of light still moves as a beam of light back and forth between you.
I don't think this explanation works, because if a ship cannot outrun it's own light cone
while at warp, then warp speed is no longer FTL, because the ship will not be able to outrun a beam of light in any reference frame.
I think it is best to ignore relativity when dealing with warp speeds.