How do I properly shuffle a Rubik’s Cube?
The best way to ’scramble a Rubik’s cube’ is to do it the way the World Cube Association gets their cubes ready to be solved. To do this they run a computer program (which uses a random scrambling algorithm) and it tells them how to set up the puzzle. The program (and details) can be found at my source.
As for your second question I’m not quite sure how to set this up without programming a application to calculate it up. It would have to be the mathmatically largest ‘distance’ (via a series of moves) that you could get each color set away from each other. I’ll do some more research for you.