If he is running outside the baseline as he legally should, it's a foul ball. If he happens to be in the field of play he's out.
Yes, they are allowed to advance a base.
There are many characteristics in baseball. The main characteristics are pitching the ball to the batter and then the batter running after hitting the ball.
The batter is supposed to stay within the rectangle when running to first base. If the batter is outside the box and gets hit with a thrown ball, they can be called out for running outside the baseline.
In MLB, according to Rule 6.05(d) the batter is called out. The play is scored as a strikeout.
a steal or balk
It is called a foul
Nothing happens to the batter. The runner who interfered is called out.
No, As long as it is unintentional as ruled by the the umpirers
The batter was bunting the Baseball.
I'm not sure if you mean "baseball" when you say "rounders," but if you are, nothing happens if the batter drops the bat in baseball.
If a batter is hit by a pitch, that batter automatically advances to first base.
if another player has touched it besides the batter your are not out if it is straight from the bat you are out if another player is holding it you are out