in your out at home question, If the out is a force, No hit.
If the runner was not forced to advance and just made a bone head base running mistake. then could give a hit.
The job of the batter is to advance the runners.
IMO The scoring is pretty clear cut, even when the baserunner may be to blame..
Scoring at times can be hard luck
MLB RULES
9.0 rules of scoring
9.05 base hits ...
9.05.(b) The official scorer will not credit a base hit when a:
9.05.b.(1) runner is forced out by a batted ball, or would have been forced out except for a fielding error;
9.05.b.(2) batter apparently hits safely and a runner who is forced to advance by reason of the batter becoming a runner fails to touch the first base to which such runner is advancing and is called out on appeal. The official scorer shall charge the batter with a time at bat but no hit;
9.05.b.(3) pitcher, the catcher or any infielder handles a batted ball and puts out a preceding runner who is attempting to advance one base or to return to his original base, or would have put out such runner with ordinary effort except for a fielding error. The official scorer shall charge the batter with a time at bat but no hit;