These are about the toughest questions we've ever gotten. I'll work backwards, from the easiest.
3) Actually a qubit doesn't have to be in either 0 or 1. It can be
in combinations of part 0 and part 1. So can various classical systems,
although digital computers are built around bits which are designed to
be in only one of two states. A classical part (say the charge on a
capacitor) which can take on a continuum of values can be used in an
analog, as opposed to digital, computer. One example would be a pointer
which could point at different angles. You could use a pointer like
that to encode 1001101 by pointing at the angle 10.01101 degrees. Of
course, a little jiggle would make errors in the reading. That's why
analog computers are used only for special purposes, not to substitute
for digital computers.
But now I have to tell you the strange part. If you have two
separate classical parts, whether analog or digital, each one can be in
any of its states. For two qubits, the states they are in can be
entangled. The first one can be in both 0 and 1 and so can the second
one, yet due to entanglement you can have only the states (0,0) and
(1,1) possible, not the combinations ((0,1) and (1,0). Or you can have
the opposite entanglement. That's what makes these qubits and not just
classical analog parts.
2) The EPR effect, now repeatedly confirmed by experiments, says
that the crazy entanglement we just described is real. If you 'measure'
the first qubit, you might find either a 0 or 1. It's completely
unpredictable. The same is true for the second qubit. And yet, the
possible pairs of results are completely determined by the
entanglement. Nature doesn't know either of the results ahead of time,
yet it knows the connection between the results.
We absolutely do not understand how this happens. It may be the deepest mystery in the universe.
At any rate, no information is transmitted from one place to
another when these measurements are made. That's because the results at
both ends are purely random.
1) The quantum states are represented as something called vectors,
sort of like arrows in 3-dimensions. Unitary operations are like
rotations, preserving the length of the arrows. They are indeed
reversible, at least in principle.
If you try to describe the quantum state of some system that's
interacting with other things, different parts of the system's state
get entangled with different versions of the other stuff. Then the
quantum description of the system breaks up into the equivalent of
different pieces of quantum state, which are no longer connected to
each other. However, if you write a quantum description of ALL the
interacting stuff, the quantum state does not break up, at least
according to the unitary time development.
Trying to make sense of what becomes of a quantum state, e.g.
whether the overall development is truly unitary or not, is known as
the measurement problem. There are a variety of ideas about it, ranging
from crazy to crazier. There are many books on the topic, but for a
non-specialist I recommend E. Squires' book "The Mystery of the Quantum
(published on 10/22/2007)