For number 3 and NBA players, wouldn't the fact that having to be so tall would trump the age effect? Being 7 feet tall is an extremely rare statistic event, so whether the player is born in January or December isn't material.
A lot of this can be explained by the differences in the leagues and how they group kids by age.
NHL: You play by year. An under 17 team (U17) this year will have everyone born in the 1997. If you're born in Jan-May, you're already 17 playing in the under 17 league. This is a small advantage. It is a huge advantage in the U6 league and gets the earlier born into club teams and youth programs where they receive special attention and better hopes of a professional future. This same model applies to soccer.
Basketball: Basketball is unusual in that a tremendous amount of the players growth consists of playing pick up games against other players. Playing against better players is simply a matter of being able to keep up. It is the closest to a meritocracy among these sports.
NFL: Football is unusual in that it is not club dominated but scholastic in nature. The age cutoff is typically Sep 1st, or nearby. I would be curious about those in the July/Aug band and how many were held back a year so they could be older
