We don't have a good understanding of what goes on beyond the event horizon. General relativity tries to explain the curvature of space time due to mass. This mathematical modelling could estimate the behavior of light due to its physical properties. But the key thing is, that space-time is curved so much beyond the event horizon of a black hole that light is unable to escape the gravitational acceleration towards the singularity. So as far as velocity is concerned; there are ways to estimate, but physically, we have no idea what really happens "at the center" of a black hole.