Black holes are composed of matter that is so dense that its own gravity causes it to collapse. All black holes, therefore, have an infinite density. Black holes also have other interesting properties due to this infinite density. A black hole has a very low temperature because so little radiation escapes from it. In fact, the only way radiation can escape from a black hole is for random quantum fluctuations to produce a complementary pair of particles, with only one of the particles inside of the event horizon. This causes that particle to be sucked into the black hole before the particles can collide and destroy each other. The remaining particle then uses the energy from the black hole to fly through space.
Quantum tunneling is caused by the random quantum fluctuations that are present in our universe. Quantum mechanics states that any particle may have any amount of energy at any given time. If that random amount of energy is high enough, the particle can quantum tunnel. An example of this on a ridiculously large scale would be if you were to throw a penny at a wall, and the penny went through. Due to the penny's extremely large size, this would probably never have happened if for the entire history of humanity, people had been throwing pennies at walls.
Quantum immortality is the theory that from your point of view, you are immortal. Note that from anybody else's point of view, you can die. This theory works on the theory which states that there is an infinite number of universes, with a new one occuring every time an option is presented. Thus there is a universe for every possibility. For example, if you were to put a gun to your head and pull the trigger, there are technically an infinite number of possible outcomes, but we will simplify it to two: you live or you die. Now, two universes are created from this situation. In one of these universes, you will be dead, thus you will no longer have a point of view in that univese. In the other universe, however, you survive. This is the the universe you will experience. Therefore, you can not die.