Situation 1 is legal. His front foot does not have to be directly in front of the rubber, it can be in an open stance. (Casebook 6.1.3A)
Situation 2 if he steps toward third and then without stepping off the rubber, he must throw to first base. If in the fake to third he comes off the rubber, he is then a fielder and may fake or throw to first. If you consider the initial step toward third and the step toward first to be one continuous motion it is a balk.
Situation 3 - (Casebook 6.1.3I) jump turn where F1 lands with non pivot foot closer to second than the pivot foot is legal. The jump turn is considered a step. Once he does this he becomes a fielder and may make any play.
Situation 4 - I don't believe an actual fake is required, the step is all that's required. I believe the step and the non-throw is considered a feint.
Situation 5 - The step is required before the throw. A throw followed by a step is a balk.
The pitcher cannot while in contact with the rubber step anywhere but toward a base. However, for practical purposes, wherever he steps is closer to one base than another. If he is closer to first base and fakes (does not throw), then that is a balk. If he steps at a runner closer to home and does not throw, then that is a balk.
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