1.) We still don’t know whether black holes destroy information. A black hole, at its core, can be completely described by only three parameters: its mass, its angular momentum, and its charge. This no-hair theorem seems at odds with the fact that objects that can fall in — like, say, a book — contain a lot more information than that, and the laws of thermodynamics do not allow us to decrease information (or entropy) as time goes forward. While the information within a book may get imprinted on a black hole’s event horizon, eventually that black hole will decay to purely thermal radiation: Hawking radiation. What does this mean for the book’s information? Is it conserved, somehow, and entangled in the quantum morass of radiation that gets emitted? Or is it lost forever to the abyss of the black hole? Despite Hawking’s numerous grandiose claims, this question remains unanswered. The black hole information paradox has outlived the paradox’s creator. More.
See also: A Brief History of Stephen Hawking at New Scientist (homework help)
One of his books is available at an excellent, possibly memorial, price.