The Laws of the Game say that a direct free kick should be awarded if a player "handles the ball deliberately". Especially in youth leagues, referees generally determine that a player who is instinctively defending him or herself, and not gaining an advantage from using a hand, has not "deliberately" handled the ball, and therefore they don't award a free kick.
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Yes. Any time the ball is kicked, whether by accident or on purpose, it is a kick. Depending on how strict the referees are depends on if they will actually call it or not.