Yes it is okay if the positioning of his shoulders is not straight. If he makes a motion with his shoulders, that constitutes a fake and is considered a balk.
The pitcher must step directly to the base he is throwing to. If he starts to step toward third and without stopping he changes direction and steps to first, then he did not step directly. If he steps to third and stops, then he can step toward first and throw. In summary, for each step he makes, the step must be directly to one base without changing direction.
He is not required to take a big step, so if he makes a little step toward third, his front foot lands on the ground, he has legally stepped toward third. If he then steps toward first and throws, then that is legal.
I would tell the coach "He did not step directly to the base". If the coach persisted: "He did not step directly to the base." There is no need to elaborate, just continue to repeat.
I would consider a feint to be legally stepping toward a base and then not throwing to that base. I would not require any hand pumping.
Don't worry about it if you made any mistakes, you learn from it and you make fewer mistakes next time. If you know the coach and he rags you about it, just admit, hey on this one I was right, but the other one, I blew it.
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