Call For Physical Clarification-Special Theory of Relativity

I've been spending too much time staring at Hubble images, and I am now having problems with some aspects of Einstein's Special Theory of Relativity, specifically:

1.) Light shouId be observed by ALL observers at the same speed,

2.) The speed of light is a CONSTANT: c.

If these components are both true, what happens near a black hole, where even photons cannot reach escape velocity? What happens to a photon at the edge of a black hole, and what would an observer (at the edge but NOT on the photon) see?