Beautiful puzzle, beautiful! This one, I never encountered before. And so, there I was, with a paper and a pencil, waiting for an commercial interruption in the series Life on Mars to start drawing what I expected was going to be complicated graphs of handshakes when, BAM!, the answer is simple, very simple, really simple although elusive, like it should be for all the great puzzles, so to answer the first question and with all this previous text as a suitable buffer spoil warner, I hope, yes, and answering the second question, no, and the third, how I got there, well, one answer is to see an episode of Life on Mars (the one with the swinger party of 4 couples… are you getting inspiration for an adult retelling of it?), other I was going to leave to others to give… except… oh, naughty Andrew, something is smelly, why would you present an impossible puzzle to happen?… hmmm… who are I’m calling fool? Perhaps it is time to look in the mirror? So, back to the paper and pencil, to see if it impossible or not, and avoid the fool’s role to myself. In the end, the answer is the same as before to the first two questions but the answer to the third is crucial, because we might reach the right answer to the first two by the wrong way. And to show I know, I’ll have to spoil a little more and say, I shook hands with the same people as my wife, and she shook hands as many times as Mars appears on this text.

PS.: Nice of you to present only 4 couples in the puzzle, I would have entered in panic if you had presented twenty or forty couples in it
:-D

PS.PS.: Keep these amazing puzzles coming!!!!