Correct.

This is the MLB rule 10.05 (b):
The official scorer shall not credit a base hit when a runner is forced out by a batted ball, or would have been forced out except for a fielding error;.

The question is: did the runner reach the second base? If he run over the Base yes; if he was oversliding the Base no. If he got the base no force out and base hit for the runner. The runner is tagged AFTER reaching second. If the runner did not reach the second Base safely, force out at second and ...

Without the throw hitting him, R1 would have remained at 3rd and R2 at 2nd. OK. So these two advancements are due to the throwing error of the second baseman who cut off the throw from the outfield. Summarizing: base hit + 2nd on the throw + 3rd on the throwing error for the batter-runner; 3rd for ...

I guess the 2nd baseman must be charged with a throwing error with which the R1 advancements to home and R2 to third are justified. The rule states that a throw that hits a runner is an error if there are further advancements that would not be with a perfect throw. I The question is: the runner woul...

My suggestion is to carefully read Rule 10.17 of MLB rulebook. As far as the most effective relief pitcher choice is concerned, the comment to the rule reported below is self explanatory. Bye, Roberto Rule 10.17(b) Comment: It is the intent of Rule 10.17(b) that a relief pitcher pitch at least one c...

I agree with the comments. Unearned run. The proof is given by the runner in third who was never been able to score before the third defense opprtunity.
Do not forget to credit batter #3 with a sacrifice hit as no one mentioned it: Sac Hit, Reached on a throwing error by pitcher.

Agree. You never credit a stolen base as consequence of a batted ball. Fielder's choice.

If the play had been made at first (batter safe or out) and the player from third advanced home, that run would be scored as a fielder's choice. Just a small correction to the perfect reconstruction of Team_mom (from Taxi_dad ☺): if the batter was safe the passed ball would be charged to catcher; i...

Runner on 3rd. Batter swings, catches lets ball get away from him and rolls several feet from the plate. He hesitates before throwing to first, sees runner coming home and tosses to pitcher covering plate, run scores. Is this an error on catcher. Throw was a little wide but if a good throw runner w...

Surely not. In any case a possible error is exempted when the ball is recovered and a FORCE out is made. Scoring is 41.