[Adam]

dmote:
Your first scenario is one of much debate and discussion; it's not well covered in the rule books.
Some would say to do the whole throwin over. Others say the game is over, no basket. Some would say if the official has definite knowledge of how much time should have elapsed, give the team a throwin where the ball was caught. However, with such a short amount of time, it would be nearly impossible to say for sure how much time should have come off. There really isn't any way to determine whether this basket would have been good or not.

Can I see an official making the decision you describe? Yes, and I can see a whole bunch of officials disagreeing with it.
BTW, the NCAA may allow for a stopwatch to be used with replay on this. I'm not sure.
So, in answer to your questions:
Set 1.
1. Seems reasonable as an amount of time for this dilemma.
2. See above comments.
3. They shouldn't, but I think some would.
4. It shouldn't, but it probably would weigh in for some officials, depending on the level of ball.

Set 2.
1. InCorrect. Edit: sorry, I assumed there was a TO for some reason. The clock would continue to run here as it does not stop on a made basket in HS rules.
2. I'm assuming this foul was called on the defense for pushing through the screen. If so, you'll shoot the free throws in HS and college. If it was on the offense for an illegal screen, you would not shoot free throws in college, but you would in HS.
3. A TO would not affect the spot of the throwin.

Set 3:
1. Legal play, and an easy bucket to count.
2. If the tapper hits the ball with a fist, it would be illegal.