I dunno about xrays, but it is true that light slows down in media and that particles can move faster than light in that medium, that's where Cherenkov radiation comes from! (Though I'm not sure if that also just slows down the particles or what)

c is the speed of light in a vacuum. It is impossible to send information faster than c. x-rays are also just light so everything I said before also applies to x-rays.

I'm not very familiar with how light interacts with materials since it wasn't covered in the electromagnetism class that I took, so the next part might be wrong. The speed of light is calculated by looking at Maxwell's laws of electromagnetism and recognizing that it is the equation for a wave. The speed is then calculated as c = 1/sqrt(epsilon_0 * mu_0) where epsilon_0 and mu_0 are the vacuum permittivity and the vacuum permeability. Inside a material, I think the permittivity and permeability are different and thus the speed of light as determined by Maxwell's equations would be different. I know its not possible for the speed (group velocity) of light in a material to be faster than the speed of light in a vacuum because otherwise, you could send information faster than c, which is impossible.