Quick questions: javelins with dueling style and natural weapon proficiency

[ThorOdinson]

Nope, I do not ask you where in that chain the attack occurs.

The chain is the attack. This can be shown in two ways.

A) an attack cannot occur without all steps in the chain being met,

And

B) the chain is defined by the RAW as the simple structure of an attack. (Phb pg. 194)

So, an attack by a thrown weapon is an attack with a one handed weapon. Following all the steps of an attack (as no step can be excluded, as you yourself have shown), it satisfies all the conditions to meet the requirements of duellist. Therefore, the bonus damage granted by duellist applies. Q.E.D.

The Dueling fighting style requires the weapon to be in one hand when the damage roll is made.