A push is called if you push another player...usually the refs call it a foul once your arm is extended.
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If you are referring to the foul, it is when a player pushes another player usually when they have the ball.
No there isn't allowed slapping in Basketball. If you want to, you can try and take the ball away from another person while dribbiling. Just try not to hit them. Then you would get a foul.
No, it's called "blocking out" or "boxing out." Getting your defender out of the way.