Why are these moves considered best?

I'm looking at a past couple of games and trying to figure out why these moves are considered best? Please can someone explain what I'm missing?

Position 1: quite a common trick in the opening because the Bg4 is undefended and vulnerable, after Bxf7+ Kxf7 Ne5+ Ke8 Qxg4 white has won a pawn and black can no longer castle. This is a sizeable advantage for white.

Position 2: This is an open position with Queens and rooks on the board. In such a situation initiative is very important because these pieces can generate big threats. The main point of Qd7 is to prevent Rxb7 by white. If white gets this move he can attack f7 forcing a move to defend that square and getting some chances despite being down a couple of pawns. Qd7 consolidates everything nice and safely, doesn't lose a pawn, and black should be winning fairly comfortably with the extra pawns.

Position 3: Ne4 creates the severe threat of Nd6+. If hxg5 Nd6+ the black king is forced to d7 which is a horrible place for it and white can then recoup material with Nxf7 winning back a pawn and forking the queen and rook. This is a good trade off for white. 

No worries. You mean why must black play hxg5 instead of preventing Nd6? The problem is that black has no way to prevent it, which is why it is such a strong threat. Black would like to move the Ne7 allowing the Bf8 to cover the d6 square but it is pinned to the Qd8 by the Bg5. No other piece can control d6 for black so he may as well eat the bishop and hope for the best. A good illustration of tempo this...i assume black has just gone h6 and white has had the automatic thought 'he attacks my bishop, I have to move it' before playing Bxe7. It is of course usually the case that an attacked piece must move away but always have a look at other moves first. If you can do something like this where your own threats are greater than the value of the piece you are leaving attacked it will either force an advantage like here, or force your opponent to address your threat instead of capturing.