Ok, quick modern physics lesson.

Bradybaker pretty much has it, but there's a subtlety that's being missed. Einstein's theory of general relativity states that nothing with mass/inertia can be accelerated to the speed of light. It says nothing about particles that might or might not already be moving faster than the speed of light. There is no experimental evidence of these hypothetical FTL particles that I know of, but they go by the name of "tachyons" and are not forbidden by general relativity.

The definition of a black hole is any region of spacetime from within which the escape velocity exceeds that of the speed of light. Light doesn't speed up when it enters a blackhole. Light travels at 2.998E8 m/s in a vacuum. Period. It travels slower than this through various media, but it never travels faster. In fact, Einstein developed general relativity from a thought experiment he performed wherein he determined that regardless of the relative speed of an observer, s/he must always measure the speed of light in a vacuum as 2.998E8 m/s.

The world at quantum scales is not a realm where all physical laws break down and cease to exist. We have laws to describe the behavior of particles at such scales and those are the laws of quantum mechanics. Are they strange and occasionally counterintuitive? Yes. Are they incomplete? Yes. We still lack a quantum theory of gravity. Does this incompleteness make them dismissible? No. The theoretical predictions of quantum mechanics have been experimentally tested and confirmed for over 80 years. No previous physical theory has been so ubiquitously successful. Just because something is incomplete does not make it incorrect. Newton's laws of motion, for example, are not "wrong," they are simply the low-speed approximations of Einstein's laws.