Official Baseball Rules section 2.00 Definition of Terms: A fielders choice is the act of a fielder who handles a fair grounder and, instead of throwing to first base to put out the batter-runner, throws to another base in an attempt to put out a preceding runner.
This is a tricky one. The easiest way to think of it is one runner is out attempting to advance on a wild pitch/pass ball while another runner advances safely.
The reason they don't simply score it as "advanced on wild pitch/pass ball" is because the official MLB rules* state that if an out occurs on what would normally be ruled as a wild pitch or pass ball (throwing someone out at home who was trying to score on a ball that got away from the catcher, for example), then it's not actually a wild pitch/pass ball because an out was made on the play. The other runners who advance safely on the play are said to have done so on a "runner's fielder's choice."
*See the official comment for MLB rule 10.13 (Wild Pitches And Passed Balls).
Yes, it counts as an 0 for 1. The reasoning behind it, is this: A fielder's choice usually happens when there is a runner on first, and you hit a grounder. The fielder could easily throw you out at first, but he CHOOSES to get the runner out at 2nd instead. You effectively have made an out, and not reached base safely via a hit, but the only reason you're on base and not the other guy is because to the fielder, it was more advantageous to get the lead baserunner out.
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.
No.
Yes, the batter is credited with an at-bat and scored as a fielders choice.
Yes
No matter what, in a fielders choice play the batter is given and 0 for 1 in the record books. It is based on the thought that if the defense had attempted a play on the batter he most surely would have been out. You misunderstood the question. If a fielder's choice is attmpted, but all runners are save and no error is scored it's a hit ... since the fielder's choice didn't actually happen.
Yes
1. Base Hit 2. BB 3. HBP 4. E 5. Fielders Choice 6. Dropped 3rd Strike 7. Catchers Interference 8. Runners
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
It can't ... a balk can only be committed by a pitcher.
No. No error can ever be given when there is an out made on the play.
It does not count as an at bat
Nope. It's a stolen base.