No, but you’re close. Thorin mentioned the Arkenstone earlier. When the whole party had to go into the Mountain, after Smaug attacked, Bilbo was scouting ahead and found the Arkenstone. (Smaug was already dead, but they did not know this.) He rationalised it as “the dwarves said I could pick my own share” but he was guiltily aware that Thorin surely did not mean to include the Arkenstone.
Concerning the Elf-king, Tolkien says in The Hobbit that the Wood-Elves were not as noble and wise as the Elves of Rivendell; they were a different kind who never went into the West in antiquity. However, they were still Elves for all that and therefore Good People, but Thranduil was no less likely than any other King to seize a chance to increase his wealth if he saw a chance to.
The first he knew about Thorin’s real business was after Thorin reached Lake-Town; Elves were there and later relayed the news to him, and he was evidently prepared to charge Thorin the father and mother of all highway tolls if Thorin came back that way with dragon-gold. When he heard the news that Smaug was dead he assumed the hoard was unguarded; he and his army diverted to the ruins of Lake-Town when they learned how badly off the Men were. And it’s worth mentioning that, when they knew Dain’s reinforcements were on the way, the Elf-king was unwilling to start a war over gold even when it when it was the best chance of keeping the Iron Hills dwarves out of the Mountain.
In Tolkien’s legendarium, there were Light Elves, Dark Elves, and Grey Elves. Light Elves were those who had seen the light of the Two Trees, before the Sun and Moon. Dark Elves were invited to come to Valinor and see the Light, but refused to go. The Grey Elves came out of a sort of special case: Thingol, one of the great Elvish patriarchs, started on the journey to Valinor, but on the way he met and fell in love with Melian the Maia, and decided to stay in Middle-Earth with her. So he and his people never saw the Light, but they did have the guidance and teaching of Melian, which put them a fair bit ahead of those who simply refused to go. The Elves of Mirkwood descended from this group.
One point of irony, by the way, is that all of the Light Elves in Middle-Earth were there only because of dark deeds in which they were involved. They came back over from Valinor, against the advice of the Valar, because of a rash oath Feanor had sworn, and in the process slew many of their own kin. Galadriel was the last of these, and was basically working off a self-imposed atonement.
Ahem. Elwë, later known as Elu Thingol was Caliquendi, an elf of the light. He, along with Finwë and Ingwë journeyed with Oromë to Valinor and saw the Two Trees.
All 3 then returned to their people, to pursuade them to go to Valinor.
Not the last (although the last of the leaders of the people, agreed). Gildor Inglorion (“Three Is Company”) refers to himself and his company as “Exiles”, of the house of Finrod, and is kin to some of the Light-Elves in Rivendell. Galadriel, btw, was innocent of the Kinslaying, but fell under the Ban because she went and separately joined the rebels.
She was indeed innocent of the kinslaying, as she marched with the people of her father, Finarfin. They came late to the battle, and did what they could to stop the violence and aid the wounded.
But to say that Galadriel went to ME separately is to rely on JRRT’s writings after he finished LOTR, where he was in the process of reconsidering what passed for his canon about the origins of Galadriel. In the published Sil and LOTR, these ideas had not been introduced, and she was indeed part of the host of Noldor who marched out of Tirion upon Tuna (silly name for a city, I know.)
