Bunted Balls - 2 Questions

Question
Two questions regarding a bunted ball, both are calls that an Umpire made in games I coached:

1. A batter bunts a ball and it immediately hit home plate before rolling into fair territory. The Umpire ruled that on a bunted ball that immediately strikes home plate, the ball is foul, no matter where it ends up after striking home plate.

2. A batter bunts the ball and the ball comes to rest in the part of the batter's box that is in fair territory. The umpire ruled it a foul ball b/c it came to rest in the batter's box, even though the ball is clearly in fair territory.

What are the real rulings on both of these situations, thanks!

Answer
Question 1 the umpire was not correct.  If the ball is first touched on or over fair territory fair ball if on or over foul territory, foul ball.  It doesn't matter if the ball hits the plate.

Question 2 again incorrect, see reasoning for question 1.  Part of the batters box is in fair territory, part is in foul territory.

Tom