it is scored a wp the batter doesn't get RBI
No RBI is awarded. Nor is one awarded if a run scores via a balk, passed ball, ground into a double play, error, and maybe some other things I can't think of.
Yes. Even though the run is not charged to the pitcher, due to an error by his defense, the player scoring is credited with a run scored. However, the batter may or may not receive a Run Batted In. The official scorer will determine if the runner, would have scored, regardless of the error, and then determine if the player should or should not receive a RBI.
The play is dead, the runner that was hit is out, and the batter reaches first base and is credited with a single.
Most likely it is neither a hit nor an error. In most cases this would be scored a "Fielder's Choice". It could be a hit if, in the scorers judgement, the batter would have beat the throw to first had the pitcher not hesitated to hold the runner. It would not be an error unless the pitcher bobbled or misplayed the ball. To clarify, a "Fielder's Choice" can be recorded even if an out is not registered.
The batter is out, scored 2u, not a strike out.
A batter gets an RBI if his groundout scored a runner. The only exception is if the batter hit into a double play, in which case no RBI is given. Of course if the runner scored on an error, and not on the groundout, there is also no RBI.
Yes as long as the runner advances Assuming you mean the runner tags up on a fly ball and advances to second, it is not scored as a sacrifice, but, simply as a fly out and the batter is charged with a time at bat. If the batter bunt a ground ball, the runner would not be required to "tag up" to advance and the batter would be credited with a sacrifice. If the batter is attempting a sacrifice bunt and pops up and the runner, tags up and somehow advances to second the batter is not credited with a sacrifice.
The batter could be credited with an RBI if, in the scorers judgment the base runner would have scored had there not been any overthrows (errors). For example, the batten singles and the runner is on third and scores, then the overthrows occur. The batter is credited with one RBI. In your original question, the batter would, in no case, be credited with an RBI on his own score.
the run is unearned unless the runner would have later scored anyway
2 unassisted. Any batter or runner called out on account of a rule is scored as the action of the nearest player.
The batter is awarded a single. MLB Rule 10.05(5) states that a batter is credited with a base hit when: "A fair ball that has not been touched by a fielder touches a runner or an umpire, unless a runner is called out for having been touched by an Infield Fly, in which case the official scorer shall not score a hit".
It is scored as a strike out for the pitcher (as far as the pitcher's stats) but not an out against the team at bat. The base runner's advance to 1st is scored as a passed ball (error) on the cather.
The official scorer would have to determine if the throw was catchable. If the throw was, then the error would be on the first baseman and he would be charged as such. If on the other hand the throw was a bad one and the first baseman had to reach and could not catch the ball, then the error is on the pitcher. Only one error would be charged even though the base runner advanced two base and scored.