1) That's the name of his book, and Hawking did propose some of the first arguments that seemed to show that information could be lost in a black hole, but in reality Susskind didn't argue with Hawking a large portion of the theoretical physics community (mostly quantum & particle physicists) were arguing with another (mostly relativists and astrophysicists in cosmology).
2) The reason Susskind, Hawking, and others frame the issue in terms of information rather than matter or energy is because it is the most abstract manner in which to conceptualize, frame, and formalize the issue. Even more than energy, information is not something that we typically think of as "physical". The problem, historically, with fundamental conservation laws like the conservation of matter or the conservation of energy was that they kept being violated. Laws of physics that were so appealing not only to natural philosophers of antiquity or in the middle ages but to early modern scientists as well turned out to be wrong. Energy was a concept long in the making, but this turned out to be a good thing. It was not clear how to relate different types of energy initially (and some things that are now thought of as types of energy used to be considered something else entirely- it used to be thought, for example, that heat was a substance). So in different areas of physics and chemistry different laws and principles governed processes that seemed to be quite different yet were related to energy.
The reason this turned out to be a good thing was that it allowed us to more easily save energy conservation from being relegated to the dustbins of antiquated, incorrect ideas about the nature of reality the way that e.g., the caloric theory of heat or phlogiston were. Matter was not as lucky. Matter is very intuitive as something that has substance and thus it is not easy to think of as something that can be "potential" in a system without having any substance itself, or can be transformed from something material into...? Energy, however, always was defined in certain cases for book-keeping reasons. Potential energy or the ability to perform work was in some ways quite intuitive and could be related to by 16th and 17th century mechanics working with pulleys and whatnot, but it is not an intuitively physical property of anything.
This matters because when it turned out that ancient ideas about the inability for matter to be created or destroyed were wrong, and then when later ideas about the inability for energy to be created or destroyed were also wrong, we could tweak the laws regarding the conservation of energy to reflect newer principles by changing how we kept the books. Eventually, though even here this process breaks down and the kinds of ways in which energy can be both created and destroyed are so numerous that it becomes misleading and vacuous at best to say that it is always conserved. Information, which can easily by material in nature or insubstantial, is much better. It is highly abstract. It was defined mathematically outside of physics in the first place. And anything which can be described by equations in physics can therefore be related to the mathematics of information theory (also, information theory has its roots in thermodynamics and statistical mechanics, so that helps too). Finally, you don't have to pretend that when 2 or 3 or twenty billion photons emerge sponatneously in some subatomic interaction while some subatomic particle vanishes completely that somehow energy has been "created" in the form of 2 or twenty billion photons out of the destruction of the subatomic particle (which is difficult enough to swallow even without getting into the fact that there would be no difference in energy creation if there were two photons or twenty billion).
If and when it turns out that information can be created or destroyed in ways that currently are impossible or at least can't be accounted for by modern physics, it will be easy to find out how the new transformation laws or symmetries or whatever it is that is necessary to describe these processes can be consistent with whatever new form of information conservation will be derived.
The problem with information loss and black holes is that there is no such method or methods. We cannot deal mathematically with the kind of information loss Hawking and others have proposed may be possible. So were they correct, and spacetime geometries trumped quantum principles, then we'd have to change most of the fundamental structures of physics without much guidance.
That's the only challenge Hawking and others proposed. And as it is so abstract and theoretical that only someone working in relativistic quantum computing could possibly claim it is remotely related to "practical" applications (I heard a speaker in that field claim this at a conference), it only matters from the perspective in which the conservation of information is absolutely fundamental: as long as it is defined, information is conserved.
Key here is the notion "well-defined". People like to claim things about what must be true because otherwise it would violate conservation of energy, but you can only violate conservation laws, including energy conservation, in formulas known to be invariant with respect to the conserved quantity. Whenever energy is well-defined enough so that we can say it is neither created nor destroyed, then it is conserved by definition.