1. He skinned his knees climbing down the tree.
  2. He rubbed the skin off his knees climbing down the tree.
  3. His knees were skinned off while climbing down the tree.
    All these sentences OK?
    Which one is more natural to the native ears?

#1 is definitely the most natural. #2 is marginal, but sends a shiver down my spine in sympathy when I read it, while #3 is definitely incorrect.

Could you explain how #3 is wrong with its grammar points involved?

You would have to say something like “the skin was skinned off his knees”, but that sounds very redundant.

Can I say: “He skinned out/off his knees climbing down the tree.”?

I would not - the idiom is “skinned his knees”, so if you use skinned in such a similar way, it sounds like you are getting the idiom wrong. Note that “scraped his knees” is also acceptable.