1) Hexatonic - consisting of 6 notes (usually used in reference to scales). Hexachord - a chord consisting of 6 notes. The prefix "hexa-" comes from Ancient Greek, you can find a reference here.
2) Numbering system - semitones. 0 is the tonic (C in the first image), 2 is the following note (D in the same picture), as it is 2 semitones away from 0 (0+2=2).
3) PC - pitch class.
4) "Prime form" is a bit of a shaky concept the value of which I do not fully understand myself, but maybe the link will help you. You might also want to look into some of the more common compositional mutations, like inversion, retrograde or something else set-theory-related. Overall, I think the book seems too tough for you at this stage and you might want to look into something simpler. I did not know or understand most of those concepts myself before I started composing music.