I can (hopefully) answer that first question. The idea is that when a virtual particle appears close to the "event horizon" (or whatever replaces it in Hawking's model), that particle will become a real one. This will appear as a particle/antiparticle pair: one particle may escape to the outside world (because it's beyond the event horizon) and one particle may fall in. However, according to Sean Carroll, the total energy of a virtual particle/antiparticle pair is exactly zero. For the real particle, the energy can never be negative. So "if the real particle that escapes the black hole has positive energy, and the total energy of the original virtual particle pair was zero, that means the partner that fell into the black hole must have a negative energy. When it falls in, the total mass of the black hole goes down. Eventually, unless extra energy is added from other sources, a black hole will evaporate away entirely." So if you wait a sufficient length of time, particles can escape the black hole as it radiates away.