It can't ... a balk can only be committed by a pitcher.
Which choice of God's are you referring to?
No.
Yes, the batter is credited with an at-bat and scored as a fielders choice.
Yes
I've found 13. Error, wild pitch, passed ball, catcher's interference, balk,hit by pitch, sac fly, sac bunt, walk, hit, stolen base,double play and fielders choice.
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. No error can ever be given when there is an out made on the play.
In baseball the only defensive player allowed to be in foul territory is the catcher. Otherwise it's a fielders balk.
It does not count as an at bat
Nope. It's a stolen base.
No hit it is a fielders choice