Quick questions: javelins with dueling style and natural weapon proficiency

[ProsecutorGodot]

"Thrown
If a weapon has the thrown property, you can throw the weapon to make a ranged attack."

If the weapon is still in one hand you did not throw it and therefore did not have permission to make a ranged attack.

Where does it say that it's left your hand before damage is rolled? The attack and damage rolls happen simultaneously as far as mechanics are concerned.

This seems to be the crux of your argument, but simply quoting this doesn't prove your case.