Bilbo´s treachery

[Inziladun]

On the face of it, I can see the source of your outrage. However, I disagree.

Bard's legal claim to a share of the treasure seems solid, as items from Dale were mixed in with Erebor's, the only question being the size of it. A moral share would also appear honest, as 1.The dwarves had awakened Smaug, who destroyed Lake-town; 2. Lake-town had befriended the dwarves and had given them food and other provisions, and 3. Bard was the descendant of Girion, the lord of Dale, and the slayer of Smaug.
No, Thranduil had no stake in the hoard, and it might have been better if the elven-host had stayed out of sight when Bard parleyed with Thorin, but Thranduil was there out of friendship with Esgaroth, and pity for them in their time of need.

Bilbo's dealing with the Arkenstone was borne from a hobbit-like wish to avoid conflict, especially one over gold. The rightness of at least Bilbo's intent in taking the Arkenstone and handing it to Bard would seem to be proven in Gandalf's reaction: "Well done! Mr. Baggins!"

Bilbo's stated preference to die defending Thranduil might stem from the mere "oddity" (as a hobbit) he displayed in his affinity for Elves in general.

As for Bilbo giving Thranduil the necklace, Bilbo himself said he did it to pay for the food he'd eaten in the elven-halls. He wasn't necessarily ungrateful. We don't see him giving away the mithril coat, after all.