**Mary was not conceived free from sin. **
Again you are mistaken. Would The Angel Gabriel call her "full of grace" or some Bibles these days says, "highly favored one" for nothing?
She had no sin so that she could be the New Ark of the Covenant and carry Jesus within her womb. Does it make sense that God would put Jesus, sinless as he was, inside a woman who had sinned? I think not.
It's a passive participle. Kecharitomene is not what Mary did. It's what she was given from the One who gives grace. A more accurate translation, in my opinion, would be "who has had grace shown to her."
Does it make sense that God would put Jesus, sinless as he was, inside a woman who had sinned? I think not.
Does it make sense that Jesus would become a man, but remain fully God? Nope. Did it anyway. I find your argument as advanced by Catholics to be utterly unconvincing. Why is logic applied in that place when it cannot be applied to the Incarnation at large? If one can't explain how Jesus was fully human and fully God (for just one aspect of the Incarnation), why do we feel the need to explain Mary's state in relation to sin?