ANSWERS: 3
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No. The only time the ball must be thrown to first is if a lefty makes a pick-off move without stepping of the rubber (so not relevent here).
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Once a pitcher steps off the rubber he becomes a fielder and doesn't "have" to throw the ball anywhere. So no balk. While on the pitching rubber, a pitcher is allowed to fake a throw to 2nd or 3rd but cannot fake a throw to first. If they do fake(doesn't matter if they are right or left handed) then it is a balk.
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tibear has got it right. You may fake a throw to first if you step off the rubber first. While on the rubber, you must make the throw; otherwise it is a balk. You may while on the rubber fake a throw to 2nd or 3rd provided those bases are occupied.
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