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.
Yes, the batter is credited with an at-bat and scored as a fielders choice.
Yes
Yes
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
The duration of Stealing Home is 1.63 hours.
No, stealing is not a trait of Autism. Stealing is a personal choice not a behaviour as a result of a neurological variation like Autism.
Stealing Home was created on 1988-08-26.
Nope. It's a stolen base.