Anytime the batter is put out at 1st base on a batted ball it is not considered a fielders choice, it is simply a put out. Now in your scenario if the catcher would have thrown home and the runner coming from 3rd is out and the batter is safe at 1st, then in that case it would be a fielders choice
Yes, the batter is credited with an at-bat and scored as a fielders choice.
fielders choice
No..these are two different official scoring designations and have no relationship to each other. See Official Rules of Baseball on steals and fielding scoring methods.
Yes, the batter will usually be given an RBI on a Fielder's Choice in the event of a run scoring the only way the home team's official scorer will not give him an RBI on a Fielder's Choice is in event of the runner in the scorer's viewer not originally being able to score on a player and was only able to do so as a result of the defensive team's miscue.
No hit it is a fielders choice
No. This would be a fielders choice and would not count as a hit for the batter.
I AM A COLLEGE BASEBALL PLAYER ALL INFORMATION HERE IS 100% TRUE. A fielders choice does not count as a hit for the batter even though the batter reaches base safely. It counts as an out for the hitters batting average but RBI's, runs scored, stolen bases and any other effects of the batter reaching base safely count. In essence a fielders choice counts as an out because the fielder could have chose to get the batter out or another runner which means there was an out on the play. Also, you cannot assume a double play even if the ball hit was the easiest 4-6-3 which the fielders made an error on.
No.
A fielder's choice is when a fielder has choosen to make an out on another runner on base when he could of gotten the batter/runner out instead. The batter/runner is safe, therefore reaching base via a fielder's choice. Please note that this counts as an at-bat and goes against the batter's batting average.
Yes
Yes
Earned. Unearned runs only apply to cases where an error allows a runner to score where they otherwise would not have.