“How is it legal when a man is on first and pitcher turns toward first in the throw toward second.”
If the turn was passed 1B and continuous toward 2B with a free foot step toward 2B it’s legal. Can you quote a rule that it violates?
“He held the ball and didn't throw.”
A feint does not require a throw or arm motion, only a step.
“Runner went back to first. How is it not a balk?”
It’s not a balk to throw or feint to an unoccupied base to drive back a runner who’s going there or gives the impression of going there.