1. Does Thorin appreciate the gravity of what he has just said? Can he be unaware of the history of the Noldorin? Do dwarves take oaths less seriously than other folk in Middle Earth?

Dwarves take oaths very seriously . . . very, very seriously! And they are unmovable like stone. I doubt he considers the history of the Noldorin even though he is aware of them. Durin’s Folk ever made it to Beleriand; they were mostly confined to Misty Mountains until the Third Age. However, Celebrimbor, son of Curufin (son of Fëanor and most like him in crafting ability), settled in Eregion in the Second Age. They had great friendship and trade with Durin’s Folk. Celebrimbor was the forger of the Rings of Power and whom Sauron beguiled in friendly guise. Yet how much history was exchanged between is never discussed.

All the same, in the mood Thorin is in, I would doubt any such thoughts of the Noldorin and the consequences of their oath have even the slightest moment of visitation on his mind. Al thoughts seem totally driven from Thorin’s mind accept the Gold and the Arkenstone. No consequences surely of what may befall from such an oath.

Q: If events had gone otherwise in the Battle of the Five Armies, would Thorin have sought vengeance from Bilbo?

What a good question. It never occurred to me that Bilbo was under that serious of a threat. Not like it would have in the Silmarillion. Of course, there was never any doubt, because the mood and actions of the Sons of Fëanor were often demonstrated, right from the beginning of the Oath and that story was totally different in scope and tone.

But here, I never thought that Bilbo was in danger of a serious nature, close, from Thorin. It just felt that in the context of this story. Bilbo would be spared from vengeance by Thorin, because he is the hero and must go home in the end (it’s a children’s book after-all). Basically, it just never "felt" that serious like it does in the Silmarillion, or in LotR. It gives me pause foe thought to considering Bilbo’s danger in a perilous plight relative to what Oaths mean in ME.

2. Assuming Thorin's promise is to be taken seriously, is he justified in making it? Fëanor, the greatest artisan in Arda, poured all his creativity into the Silmarils. Thorin's only claim to the Arkenstone is that his forebears "found" it under the Mountain, and had it stolen from them by Smaug.

I don’t think anyone is justified in such an Oath of murder and vengeance. Especially over and object, even Fëanor (accept against Smaug, a monster of Morgoth, of course : -) ).

Q: Is anything other than greed operating here?

Here is a list:
Thorin himself had been held to an Oath by his Grandfather, Thrór, part of what got him here in the first place.
He is under the Dragon Spell.
He is under threat of siege and war.
He is already in an unreasonable mood, quite like Fëanor.
The Arkenstone represents all that this ancestors died for, and his home as well . . his rightful heritage.

It is about more than greed for an object, it’s about the symbolism and meaning of the line of Durin. It would mean regaining all the former glory of the kingdom of old and restoring the pride of his family and his father and his grandfather.