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
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.
A character proficient in simple and martial weapons is proficient in all PHB weapons. For them, other individual weapon proficiencies (like Dwarven Combat Training) don't do anything. There's no difference between a Human Fighter and a Dwarven Fighter in terms of weapon proficiencies.
However, some classes only get a limited number of weapon proficiencies, and this is where racial or other weapon proficiencies come into play. For example, by default a Wizard is only proficient with daggers, darts, slings, quarterstaffs, and light crossbows. A Dwarven Wizard, however, would also be proficient with battleaxes, handaxes, and throwing hammers thanks to Dwarven Combat Training. For that character, the Dwarf's additional weapon proficiencies greatly expand the list of weapons they can use effectively.
Both of those modifiers do add to the attack roll; the combined modifier is then relevant ability mod (DEX, +3) + proficiency bonus (+2) + Archery bonus (+2), yielding the +7 you see in the "Attacks & Spellcasting" section of the pregen character sheet (available from Wizards here).
(Note that the +4 attack bonus for greatsword is just the relevant ability mod (STR, +2) + proficiency bonus (+2).)