A liner that crosses 3rd or 1st in fair territory but lands in foul ground is fair. Why is a ball that hooks over 1st or 3rd in fair territory but lands outside the foul pole a foul and not fair?

Answer 1

The difference is where the ball first touches the ground.

For a ball that never touches the ground till after it has left the infield, the ONLY criterion for "fair or foul" is where the ball lands. If a ball is fair as it leaves the infield, but hooks such that it LANDS in foul ground, it is foul. If it lands in fair ground but then rolls or bounces foul, it remains fair. "A FAIR BALL is a batted ball that ... first falls [my emphasis] on fair territory on or beyond first base or third base". Whether the ball was a fly or a liner is irrelevent -- the only question is where it first hits the ground.

For a ball that first touches the ground while still in the infield, the criterion is whether it is fair as passes the base. "The ball may zig-zag, back-and-forth, between fair and foul ground an unlimited number of times. The ruling of fair or foul is not made until the ball finally comes to a stop, or is touched, or goes past first or third base." If it bounces OVER the base after first touching the ground in the infield (fair or foul PRIOR to the base is irrelevent), then it is fair, even if it lands in foul ground.