That would depend on the team and the manager. Most likely the third or first baseman, but in reality, whoever's in the best position to do so given the game situation at the time.
Also, it would not be a stolen base to advance on a pass ball.
another player
There are two situations. (1) If the catcher (or any defensive player) has possession of the ball the runner (Rule 7.08(a)(2) the runner is out if "the runner does not slide or attempt to get around a fielder who has the ball and is waiting to make the tag." In addition, if the umpire judges that the runner was malicious and trying to injure the fielder (including the catcher) the umpire may eject the player. However, if the catcher does NOT have possession of the ball and therefore is not waiting to make the tag, the catcher is guilty of obstruction (Rule 2.00, definition of obstruction). If the umpire makes this judgement, the runner would be awarded the base to the runner. This does not give the runner free license to slam into the catcher. Again, if the umpire judges the runner was malicious, the runner would be awarded the base (including scoring the run) and then the umpire may eject the player. In addition, if the umpire judges that the catcher was malicious and was malicious in their action (causing injury to the runner), the catcher may be ejected. So the bottom line is that the runner and catcher are expected to avoid malicious contact.
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.
When the batter is standing on the plate.
A home plate collision is usually the case of a base runner that was on one of the bases trying to reach home plate in order to score while the other team's Catcher is trying to block home plate in order to prevent the base runner from touching home plate in an effort to prevent a run from scoring and the runner and the base runner usually slides into the Catcher that is blocking home plate which is what one example of a home plate collision is.
A balk can only be called when the ball is live. If a batter has been awarded time out, then play has stopped, and a balk is impossible. It's safer for the pitcher to complete the pitch, just in case the batter isn't awarded time out.
He's safe if he touches home before the catcher picks it up and tags him. If it was a force at home then he's out as soon as the catcher touches home plate.
A defensive inning (1/2 inning actually) is when the players are in position in the infield and outfield with the defensive pitcher throwing the ball to the catcher trying to not have the batter (offensive Player) hit the ball.
You start running when the pitcher pitches the ball and then you make it to the bag before the catcher can throw it to the base you are trying to steal.
You can't steal first base. It's easier to steal second base off of a right handed pitcher because the right handed pitcher has his back to the runner on first, and therefore has a harder time trying to pick the runner off.
This is umpire's discretion, but usually if the runner is in the runner's lane (the two parallel lines starting half-way up the foul line between home plate and first base) the runner will not be called out. However, if in the umpire's judgment the runner is in the runner's lane but is deliberately trying to interfere with the throw, the runner can be called out for interference.
It's ruled "caught stealing," and scored 2-6 if the catcher throws to the shortstop, 2-4 if the catcher throws to the second baseman, etc.