1) I guess the RLUDFB notation is pretty standard, but the part about
using lower case letters to represent inverses isn't. I find it
pretty distasteful and much prefer using "'". This has the added feature
that you can write: (RLU)' to indicate the inverse if RLU. (I KNOW that
it is just U'L'R', but sometimes one wants to make the distinction.)
2) Yes, lots of things are known about the group and its subgroups.
Start by reading old cube-hackers mail while you wait for your copy
of Singmaster to arrive.
5) Yes, there is an easy way to tell if a cube is solveable without
actually trying it. Here it is:
Three conditions must be true: a) The sum of the rotations of the
corner cubies must be a multiple of 360 or 2 pi (depending on how you
count!). b) The permutation of the faces of the edge cubies must be
even. c) The permutation of all the cubies must be even.
8) Yes, they are real orbits.