There is no set rule that states this. But in practice, most runners do this because the ball is live and they could be picked off.
yes, the base runner stealing does get credit for the stolen base.
NO
There are a few times a base runner may advance without fear of being put out. If the base runner is forced to the next base by a batter/runner being walked or hit by a pitch and for an illegal pitch being called on the pitcher.
Generally, only when there are no runners on base. However, you could also pitch from the windup when there is a runner only on third base, or on 2nd and 3rd, or when the bases are loaded. Pitching from the windup can be a problem with a runner on third because this will allow the runner to get a longer lead off the base than the lead the runner will get when the pitcher pitches from the stretch.
The rule is rule 6.05 the subsection is (j). Here is what it says, "After a third strike or after he hits a fair ball, he or first base is tagged before he touches first base" In a tie the runner or the base is not tagged BEFORE the runner touches first so it can be interpreted as a tie goes to the runner. But it really is that the base or runner must be tagged before the runner reaches the base. Rule 6 applies specifically to the batter. Rule 7 applies to all runners. Rule 7.08 subsection (e) states that: Any runner is out when He fails to reach the next base before a fielder tags him or the base, after he has been forced to advance by reason of the batter becoming a runner. In this situation, the "tie" goes to the fielder. So putting these two rules together, a tie goes to the batter/runner at first and to the fielder for all other bases. In actual practice, umpires are instructed that there is no such thing as a tie and that they must determine what has happened first. Well actually according to Tim McClelland, MLB Umpire Crew Chief, a tie does not go to the runner, in the rules it states that a runner must beat the ball to the base so in fact the tie does not go to the runner.
Yes, the runner would go back to 1st base if the batter fouls off the pitch.
no they do not
missed third strike No, a Wild Pitch.
when theres a base runner on a base.. the batter hits the softball and trys to get to a base while the base runner at 3rd or 2nd run home and get a point
yes, on an illegal pitch the upmire will let you advance a base.
intentional walk?
On a dropped third strike, if there's a runner on first and less than 2 outs than the batter is automatically retired, whether or not the runner from first was stealing on the pitch. If there are 2 out, the batter can try to reach base, and the runner from first would be forced to try to advance to second. As on any other pitch, a runner can always try to advance, but would only be credited with a stolen base if he left the bag when the pitch was thrown, not after it was dropped.