Hmmm... I disagree, there have never been more than 4-5 rightees per teams that I`ve played on. This year, NHL shooters have been approximately 65% to 35% in favour of the lefties, and keep in mind that teams try to have at least a few right-shooters for the powerplay and right wingers / right dee.
However, I think this is also going to change, as sport shops aren't making straight blades anymore. Dad first gave me a plastic stick with a straight blade when I was starting to play on the ODRs, and eventually I just went into something natural. Parents now tend to have their own ideas as to what determines a left/right shooter. Concensus here seems to be that if you write with your right hand, you shoot left, but my brother is right handed and shoots right as well, so you never know. It also depends on the first hockey stick that you buy or is given to you, you kind of just get used to it.
True on the pushing the puck forward with one hand when you're on a break. I believe the top hands serves more for stability/precision, as the left hand really drive the stick, forcing it to hit the ice (at the height allowed by the right hand) and bend so that it rockets the puck away when it snaps straight again.
Think of carving, exactly the same :D