Batter's Interference is if the batter in question steps in the way of the Catcher that'll prevent him from throwing to a base.
If the batter attempts to block the catcher from throwing to third base, or if the batters obstructs the catcher in the process of throwing to third base.
The catcher is allowed to touch the batter while throwing to any base. However, the batter must not move into the catcher's path. If the batter does and the catcher makes contact with the batter, it is called as Interference. If Interference is called during a steal attempt, the runner must go back to their original base.
When there is a dropped 3rd strike
If the batter showed signs of trying to move out of the way to give the catcher a clear lane to throw then neither the batter or the runner it out. If the batter did not move at all to provide the catcher a throwing lane, then the batter is out, but the runner is safe.
A catcher is stationed behind the batter and in front of the umpire. His job is to tell the pitcher what kind of pitch to throw, and then catch the pitch. He is also responsible for throwing runners out who are trying to steal bases.
Only if it is on a third strike. That would be considered a foul tip and, by official rule, is different from a foul ball. A foul tip is when the catcher catches a ball that is 'tipped' by the batter and the ball goes straight back into the catcher's mitt. If the catcher drops the ball it is considered a foul ball and not a foul tip.
A foul tip is considered to be when the batter swings and the bat barely touches, or tips, the ball. The ball goes straight back into the catcher's mitt. A fly ball is when the batter makes contact and the ball goes up into the air for a significant distance. If a catcher catches a foul tip with less than two strikes the play is simply considered a strike and not an out. But if the catcher catches a foul tip when the batter has two strikes, the batter is scored to have struckout.
Throwing out the runner means that the batter hit the ball and a fielder fielded the ball and got the batter out running to first. It could also mean that the catcher threw the ball to second base when a girl was trying to steal and got her out. The same thing applies to third base.
The catcher, and behind the catcher is the Umpire.