1. Raise your hands on your head.

Question

2. Raise your hans over your head.
3. Raise yor hands above your head.
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(What will be the right position after the listeners do as they are told? Are the following positions right?)

In #1, the hands will be on their heads.

In #2, ther hands will be over their heads, not above their heads. (Their hands will be right above their heads.)

In #3, their hands will be above their heads, not over their heads.

Answer 1

Your interpretation of 1 is correct.

The prepositions "over" and "above" mean the same thing in these sentences. There is no difference.