[RPG] Does the same fighting style stack with itself

I'll get the simple bit done first - you're right, nothing in the Thrown property turns a melee weapon into a ranged weapon. It's a melee weapon you can use to make ranged attacks, so the Archery Fighting Style, which says that

You gain a +2 bonus to attack rolls you make with ranged weapons.

can never apply to it. It can apply to darts, because they are thrown ranged weapons. This was also confirmed in a recent Sage Advice column:

Does the Archery fighting style work with a melee weapon that you throw? No, the Archery feature benefits ranged weapons. A melee weapon, such as a dagger or handaxe, is still a melee weapon when you make a ranged attack with it.

Now for the Dueling Fighting Style. Here, I have to disagree with you - when you roll damage for a thrown weapon, you aren't wielding that weapon in one hand. You were wielding it, then you threw it, then it hit. If you were still wielding it when it hit the target, it would be a melee attack. (Unless you threw it, then teleported across the battlefield and caught it right when it hit them, which sounds cool, but doesn't seem particularly useful.)

"Wielding" is a fairly nebulous term, so there is room for interpretation here, but personally I'm inclined to think that "wielding [...] in one hand" pretty clearly requires you to be holding something in your hand.

On the other hand, Crawford says that the Dueling Fighting Style does work with thrown melee weapons, and he's the authority on these matters.

No, you can't combine them in this way.

The key point is in the description of the Two-Weapon Fighting rule (PHB, p. 195):

When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand.

The relevant issue is this: when you take the Attack action, is there a weapon in your other hand? If there is, you can't get the benefit of Dueling. If there is not, you can't make an off-hand attack using Two-Weapon Fighting.

(Note the present tense "that you're holding in the other hand", not "that you will be holding later in the turn" or "that you were holding earlier".)