Does the photon itself have its anti-particle?
No, the photon is its own antiparticle.
If our universe was made mostly of anti-matter, instead of matter, would the laws of physics be any different?
Probably not. We should just reverse a few signs here in there in the equations :)
ha! a disagreement (See my response to @irelandscape 's question).
Cool, That might open an interesting discussion :-)
At the end, I see just this as a rewording of what is a particle and an antiparticle. Therefore, things should not change :)