Before I go into this, I got a tip from an astronomer that you should get a book entitled 'Space-time Physics' by Thorne and Wheeler. It boils general relativity down to much less advanced mathematics than I was aware was possible. It might answer a lot of your questions.

As for black holes, no, time in the outside universe would not operate in reverse. Instead, time would pass much more rapidly than it would for the observer, because the observer is deeper into the gravitational potential well. In fact, apart from being able to see the singularity at the center of the black hole, the observer would have no way of knowing that he was inside of an event horizon.