And this matters why? I don't think its our misunderstanding of photons as it might a your misunderstanding about the interaction of particles.
If the two particles somehow, through any means, were able to collide at the speeds 0.75, the force exerted by each particle would not double the amount of force when hit by another particle going at the same speed in an opposite direction in comparison two when it hits a static object. Consideration of frame of reference is important, but I think you would realize that even changing the frame of reference would have a max speed of light at 2c.
What is empty space? Our understanding of nothingness has changed drastically with new understandings of quantum mechanics and the Theory of Relativity.
Again, frame of reference is important to take into account. Since, within our frame of reference, the objects being experimented on also exist within this frame of reference and are affected in the same way, the speed of said particle can be measured unless we discover a new phenomena that effects this. However, evidence suggests that such measurements are possible.
Well, scientists were able to separate the magnetic moment of a neutron from itself: