Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion.
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What is the most essential thing to study the motion of a body?
The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.
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Can a body be in motion in the frame associated with the body itself?
A body is always at rest in the frame fixed with the body itself. A body cannot be in motion with respect to a particular frame.
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Can a body be always at rest in some frame?
Yes, a body is always at rest in a frame which is fixed with the body itself.