Yaaawn...It's pretty early in the morning to be answering questions...Oh well, no games for me today until noon!
The situations you describe are actually covered by two different rules- one about being outside the batter's box and hitting the ball and another one about touching the plate and hitting the ball.
- If the batter contacts the pitch with the bat while an entire foot is outside the batter's box lines, then the ball is dead and the batter is out. See ASA rule 7-6-D and Rules Supplement #7.
The foot must be ENTIRELY outside the lines of the box AND in contact with the ground when the ball touches the bat. If any part of the foot is touching the line, even if the rest of the foot is extended outside the line, then that is not a violation- it would be a legally batted ball.
If the batter's foot is IN THE AIR when the pitch is hit, then her foot lands on the ground outside the box after that, it is not a violation.
It doesn't matter if the illegally batted ball is fair or foul- the batter is still out on either one.
- If the batter contacts the pitch with the bat while ANY part of her foot is touching home plate, then the ball is dead and the batter is out. See ASA rule 7-6-E.
This is a little different than the other rule, in that it doesn't matter if the batter's foot is still touching the batter's box lines. Even if part of her foot is still inside the box, or touching the lines of the box, she is out if any portion of her foot is touching the plate when she hits the ball.
Hope that helps!