Yes.
No, it is not considered a sacrifice unless the batter is advanced as a result of a bunt. Also, a fly ball that is caught is only considered a sacrifice if a runner tags and scores on the play. If a runner tags at 1B or 2B on the caught fly ball, and advances one base, it is not considered a sacrifice fly.
The fielder made a decision to throw the batter out at first instead of throwing the runner out at home. This is considered a fielders choice.
Yes.
Yes
Because there are situations when a run is scored and no one gets credit for an RBI. Some examples are: 1) Runner scores on a wild pitch, passed ball, or balk. 2) Runner scores on a double play. 3) Runner scores because of an defensive error.
ed Parker isn't
No, a runner will not earn a run if scored off an error.
Interference, runner scores
No, as long as the runner is forced to go to the next base, they can be tagged out or the base stepped on. Both are considered force plays, which means the run would not count.
Batter is safe at first base, runner on third scores a run.
Yes, the Official Scorer will credit a batter with a RBI in the event of a runner scoring from third in the event of a player getting caught in a run down however Official Scorers also will have the right to not credit the batter with a RBI in the event that they do not believe that the batter would have advanced the runner on third base to home plate.
That play would be called a 'fielder's choice'. A fielder's choice is a play where the defensive player that fields the ball attempts to put out a runner at another base instead of attempting to put out the batter at first base. No hit can be awarded on a fielder's choice but a sacrifice can be awarded if the batter had turned in the batter's box before the pitch in an obvious sign that they were going to bunt. An RBI can also be awarded if there was no error on the play.