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Lee
You are asking a number of interesting and in fact difficult
questions.
The full answer to some of these question require advanced college courses.
Concerning stars formation near black holes: Most black holes are
relatively small ( no more than a few tens of solar masses) and the matter
that is falling in is coming from a binary companion star. The infall rate
is very small. I think the order of a few millionths of a solar mass per
year. I do not think there is enough mass near the event horizon at any
one time to create a star. The huge black holes assumed to be at the
galactic core long ago sucked in most of the surrounding matter that is easy
to get. Most of the surrounding matter goes into orbit about these black
holes. Some of the star formation in the galactic core probably is related
to strong gravitational fields, but near the event horizon the actual
density of matter is relatively low.