How to install wood board & batten shutters on wood siding?
Your first question is a matter of aesthetics and is up to you. However, I tend to like to leave air gaps so moisture doesn't linger after rain. I'd even be inclined to use short standoff tubes to keep the shutters off the siding. 

The second partly depends on the construction of the shutters, but two screws in each of the calling battens should do. If they're very heavy shutters or of questionable build integrity you should explain that in your post.