No. If you draw a line from the back point of home plate down each foul line (to the outside edge of 1st and 3rd, then everything in front of the lines is in fair territory.
For example: If a left handed hitter lays down a bunt that falls in the right hander's batters box, in front of the plate, and inside the third base foul line, then it is a fair ball.
I hope that makes a little sense.
Fair
No. The Home Plate Umpire, the Catcher, and the Batters are in foul territory, because they are all positioned behind the foul lines.
They can but it would just be dumb. Actually, the first baseman cannot stand in foul territory. The only defensive player allowed to lineup not in fair territory is the catcher, who must take his position behind home plate in the "catcher's box", which is technically in four territory.
When the batter hits the ball into foul territory, and an opposing player catches it in foul territory on the fly.
There are lines placed to divide the foul territory and the fair territory. Any ball that lands on the foul territory will be called foul. When the ball enters the fair territory, ball is at play.
If the ball is in foul territory and hits a base runner in foul territory then it is a foul ball, so no he would not be out
If a batter gets a base hit to the outfield that would normally be a single but the ball goes through the legs of an outfielder and the batter winds up on third base, the play would be scored as a single and an error on the outfielder. Depends on the determination of the "official scorer". If the ball goes under the outfielder's legs and, in the official scorer's opinion, it could have been fielded with ordinary effort, and the batter or runners advance an additional base or bases, it would be an error allowing the runners, and/or hitter to advance. If, however, the ball goes under the outfielder's legs and, in the scorers opinion, could not have been fielded by ordinary effort, an error is not necessarily scored on the play.
The outfield wall between the left field foul line and the right field foul line is in fair territory. All other walls are in foul territory.
There are basically three areas to consider here: fair territory, foul territory, and out-of-play territory. A ground foul ball is not playable. A fly foul ball is playable if it is not in out-of-play territory. A fly foul ball is not playable if it is in out-of-play territory. An example of out-of-play territory might be a dugout. Out-of-play territory should be defined by the rule book, the ground rules, or by the umpires prior to game time.
Foul territory is that part of the playing field outside the first and third base lines extended to the fence and perpendicularly upwards. A foul ball is a batted ball that settles on foul territory between home and first base, or between home and third base, or that bounds past first or third base on or over foul territory, or that first falls on foul territory beyond first or third base, or that, while on or over foul territory, touches the person of an umpire or player, or any object foreign to the natural ground.
Most of the batter's box is in foul territory, but some of it is in fair territory, so it depends where the batted ball comes to rest.
If the ball is in fair territory, the fact that the fielder is standing in foul territory does NOT make the ball foul. the same as if a ball is foul, the fielder standing in fair territory doesn't make the ball fair.