Quick questions: javelins with dueling style and natural weapon proficiency

[Mellack]

I am saying that when a thrown weapon hits the target and deals damage it is not in one hand (or any hand).

As long as the character has permission to make a ranged attack (the Thrown weapon property gives them that permission) they can throw the weapon and roll to hit.

"Thrown: If a weapon has the thrown property, you can throw the weapon to make a ranged Attack. If the weapon is a melee weapon, you use the same ability modifier for that Attack roll and damage roll that you would use for a melee Attack with the weapon. For example, if you throw a Handaxe, you use your Strength, but if you throw a Dagger, you can use either your Strength or your Dexterity, since the Dagger has the finesse property."

But you are still not answering what I am asking.

Here I will break it down into simple yes/no questions about each step.

1. Can a character attack with a weapon that is not in their hand?

2. Can a character do damage with a weapon that in sot in their hand?

I am not asking about any "hit" or such. I am asking about two mechanical resolution steps in the game. Can you answer the simple questions please?