Hey, I'm trying to find a way to make keyframe animation and every time I move a body part it makes keyframes on all the bones.
Is there a way to disable this option so I'll get a keyframe only on the part I move? 

If I am understanding the question correctly, yes, there is.

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If you click the circled button, that is the Body Part Mode; the one to the left of it, the Full Body Mode, is what is selected by default.