What is the meaning of "Asuni va'Ychonenuni"?
Radak: The action and the preparation of fixing the limbs in the creation of man was so he can acquire Chachmah. He is unlike animals regarding stature, and intellect's control of the limbs. The heart is the king of the limbs; the brain is its appointee. Speech is via the Kelim prepared for it - the voice comes from the lungs, and it is articulated via tongue, lip, teeth and palate.
Malbim: This corresponds to his request for "Tuv Ta'am va'Da'as" (66). If Hashem will make him understand how He made and prepared him, he will learn secrets of the Mitzvos. This is because man's body, limbs, sinews, and joints, with the powers of his Nefesh, correspond to the Mitzvos. The 248 limbs and 365 sinews correspond to the 248 Mitzvos Aseh and 365 Lavim. A particular Mitzvah corresponds to each limb, like early Chachamim said.
Why did he say "Havineni v'Elmedah"?
Radak: Since You made man in a way to enable him to understand, help me to understand Your Mitzvos!
Malbim: Refer to 119:73:1:2