How to achieve shaggy/seperated layers

Firstly, I think your new style looks fantastic! 

Products that say they give "texture" and "definition" will help you here.  Do you know which ones your stylist used?  If not, some examples include: John Frieda's "Chunky Munky" (part of the Sheer Blonde range, but suitable for all hair types, as it doesn't contain any colour deposit) or Bumble + Bumble's surf spray.  There is also an Umberto Giannini product that uses sea salt to give that great chunky, layered effect and a TIGI one (sorry, I can't remember the exact names!)  Just shop around and look at what's on the shelves in your price range.

To get even sharper definition and hold in the very ends of the layers, I would recommend clay rather than wax, or a combination of wax and clay (just mix a little of each in the palm of your hand, then rub over your hair: don't overwork these kind of products as it will just look greasy).  The Sebastian range has a very good clay and also a good wax; they come in little metal pots.  Charles Worthington's is a cheaper alternative.

Good luck...

That depends on how your hair dries naturally.  If your hair's naturally straight like mine and doesn't go "poofy" without blowdrying, then you should be okay to leave it to airdry (or just use the hairdryer right at the very end, just before your hair's completely dry, just for a couple of minutes).  Experiment...and enjoy!