Not sure if this has been mentioned, but Travis Yost from TSN Analytics was on with Schopp and the Bulldog and mentioned that he knows Tim Murray was one of the first executives in a player personnel dept to embrace analytics going back to 2011
This is interesting because TM was cagey about his feelings toward #fancystats when he arrived in town. He went through this thing with White at WGR where he called them "useful," but then went on to say that, the more you know about the game, the less useful the stats become (and the less you know, the more the stats can tell you). It sorta seemed like he was throwing them some shade. Maybe not. Maybe he was just being super honest, as he so often is.
I don't have the actual studies to point you to, but the short answers are: (1) yes, including more than just shots that reach the goal and/or goalie has been shown to be a better indicator, and (2) faceoffs have been shown to have little effect on possession (it's very short lived, as good puck possession teams get it back quickly when they lose one, bad puck possession teams give it up quickly when they win one.)
As for #1, I recall reading (well, not entirely reading) a long-form piece a while back that explained in great (excruciating) detail why *all* the shots are a better indicator of a team's play than just the SOG. A few Google searches did not return the piece, though.