1.) Obviously those aren't Lassard's hands, but probably a stand-in who knows how to do trick shots (I can personally barely hit the ball, let alone do what Lassard does here). There are a lot of "trick shot" videos on youtube that might be instructional. This looks similar, for example: http://www.youtube.com/watch?v=xGmMzFGURNg
2.) It's a famous piece of classical music that I have nowhere near enough knowledge to name. I'll look into it and see if I can't come up with a title/composer. It was the same tune Harris had been smugly whistling in the previous scene when he got them suspended.
3.) I was wondering this, too. It wasn't a recognizable piece of machinery to me. I suppose the most honest and straightforward answer is that it was a prop that made it easier for Michael Winslow to do his robot impression.
Answer to question 3-They were a pair of mole grips,they are used for welding. You use them to clamp two pieces of metal togather so you you can get a nice clean weld.