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.
If scored as a Fielders Choice it will go down as 0-1 (an AB with no hit) -- tigersy2k3
Yes, the batter is credited with an at-bat and scored as a fielders choice.
maybe... maybe not!
It does not count as an at bat
It is a fielders choice
It can't ... a balk can only be committed by a pitcher.