What happens to batter when ball girl interferes with a 'live ball'?

Answer 1

Rule 3.15 of Baseball states:

"No person shall be allowed on the playing field during a game except players and coaches in uniform, managers, news photographers authorized by the home team, umpires, officers of the law in uniform and Watchmen or other employees of the home club. In case of unintentional interference with play by any person herein authorized to be on the playing field (except members of the offensive team participating in the game, or a coach in the coach’s box, or an umpire) the ball is alive and in play. If the interference is intentional, the ball shall be dead at the moment of the interference and the umpire shall impose such penalties as in his opinion will nullify the act of interference."

In other words, it's entirely the discretion of the head umpire. If a ball girl TRIED to get out of the way of a batted ball in play, but accidentally knocked it away from a fielder, an umpire might rule the ball in play. If a ball girl picked up a ball -- even if she thought the ball was not in play -- the umpire might rule that play is immediately dead and that the batter may not advance any further. If said ball girl very intentionally knocked the ball away from a fielder about to catch it, the umpire might rule the batter is out due to interference.