1. For the first inning stuff, I haven't done any statistical analysis on this, but from watching hundreds of REAL LIFE games, I would say for the first/second inning, there is some truth to this.
The reason why hitters hit better in later innings is because they are having the second or third look at the pitcher. They've seen the movement on his fastball five or six times. They know where his curveball breaks.
That really is equal to pitcher fatigue in what causes a manager to go to his bullpen. If you had Randy Johnson on the mound, you switch to a righty who throws a little softer. The contrast is what helps make the reliever so helpful.
In the first and second inning, the hitters are seeing the pitcher for the first time, and generally they are not as good as the second time through the lineup.
There are notable exceptions, like Tom Glavine, who need the first inning to find their groove, but most of those pitchers are not successful. Glavine just happens to be really good at dominating once he has a feel for the game.
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