>>14289338All EM radiation travels at the same speed in a given media, the only difference is the wavelength.
As for light falling into a blackhole it does not speed up it travels at the same speed as in a vacuum (assuming vacuum around the body). What does happen is that as the spacetime around the blackhole is stretched the light is redshifted more and more from and an outside observers perspective. However if your falling into the hole and look out things appear normal since your frame of reference has been distorted in the same way and to the same amount as an incoming photons frame has been
