|MadSci Network: Astronomy|
It sounds like you've been doing a lot of reading lately as these are some very good questions for a non-astronomer. Let me answer your second question first, since it is easier to explain. Hawking Radiation centers around the idea of virtual particles. If you follow the link I've provided, it will take you to a website with FAQ about virtual particles. These particles are "virtual" because they only exist on a very short timescale (less than 80 attoseconds), and while they exist they disobey the law of conservation of energy (because they come into existence out of nothing). [Virtual particles can exist because of a principle in quantum mechanics known as Heisenberg's Uncertainty Principle. In the case of virtual particles, the Uncertainty Principle states that one cannot measure the amount of energy present faster than a certain time interval. Thus, over a short amount of time energy conservation can be violated, for instance, by a pair of particles popping into existence from nothing.] The catch occurs when a pair of virtual particles comes into existence near a black hole (they always come in pairs). If one particle from the pair falls into the black hole, but the other one escapes, the delicate balance is disrupted and the pair can't go back to being nothing in a vaccuum.
In the meantime, the missing particle creates a lack of energy in the vaccuum and the escaping virtual particle becomes a real particle. But on a long timescale, the law of conservation of energy cannot be violated. So this missing vaccum energy balances itself out by taking energy from the black hole (this is Hawking Radiation). And using Einstein's equation, E = mc2, we can see that when a black hole loses energy, it is essentially losing mass. The escaping particle is radiated away from the black hole by Hawking Radiation.
Your first question is a little more difficult to answer because astronomers are still working on understanding the physics involved in accretion disks and jets. Most astronomers think that jets are caused by the magnetohydrodynamics going on in the disk. In simpler terms, accretion disks are thought to generate a wild magnetic field, and this magnetic field might be enough to collimate the material into the jets we see. This is still an active field of research, however, so the final answer has yet to be discovered.
Keep asking good questions,
Try the links in the MadSci Library for more information on Astronomy.