fielders choice
No.
Yes, the batter is credited with an at-bat and scored as a fielders choice.
Yes
Yes
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
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.
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
no errors on the play it would stand as an infield hit It would be a fielders choice. Baseball Rulebook section 10.06(d) A base hit shall not be scored in the following case: When a fielder fails in an attempt to put out a preceding runner, and in the scorer's judgment the batter-runner could have been put out at first base.
This depends on the situation. If the fielder threw to get the runner out and the batter reached 1st due to this, then it would be considered a sacrafice by ruling it a Fielders Choice, and no hit or error would be charged. If the batter bunted and had good placement and was able to reach 1st due to a good bunt and beating the throw, then it would be considered a hit