1) I'd say yes, but it would depend on the amount of time the ball was in the 1B's mitt. Most likely yes, it's an out.
2) Runner is out, effort must be made to avoid the ball.
3) SB, the runner is free to attempt to advance to 3rd on the throwing error, if he makes it, THAT is not a SB.
4) MLB rules are a game is official after 4 1/2 innings, 5 if the home team is behind. In either case, this game is official. IF we're going by MLB rules.
5) The run does not count, unless the runner can make it back to tag third, and then make it to the plate before a fielder steps on 3B. The runner is not automatically out, but most likely will be very soon.
-Mikey
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