Yes an error counts as an at bat, but not a hit. You would be 0 for 1 on the play, but your on base percentage goes up because you have reached base safely. Errors can be committed on sacrifice bunts and sacrifice flies. If the official scorer rules a play a sacrifice bunt/fly and an error, the batter is not charged with a time at bat. On base percentage goes down when reaching base on an straight error.
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no, if in the judgment of the official scorer a ball would have been a sacrifce fly without the error, the batter is not charged an at bat and gets credit for a sacrifice fly and an RBI
Yes. If there is an error on a hit ball, the at bat counts against the batter as if it was an out.