In the story, the lake men approached Thorin and the dwarves with a mixture of curiosity and caution. They were intrigued by the arrival of the company but also wary due to past tensions and distrust. Eventually, the lake men sought to engage with Thorin and his group, hoping to form an alliance for mutual benefit, especially given the looming threat of Smaug and the potential for shared prosperity from the treasure in the Lonely Mountain. Their approach reflects a blend of opportunism and a desire for safety in the face of uncertainty.
The dwarfs resettled the lonely mountain (Erebor) and made it their capital, they forged a strong alliance with the men of Dale (who had helped kill Smaug).
Roac, son of Carc, brought the news that the dragon Smaug had been killed in Lake-town by Bard the bowman.
Most of the population of Lake Town think the dwarves are going to kill the dragon Smaug, and so treat them with kindness, hoping to get a share of the treasure. In fact all the dwarves do is annoy Smaug, who flies down the mountain and destroys Lake Town. Smaug is eventually killed by Bard.
Because Bilbo accidentally made Smaug (The dragon) get angry at them. Their city was destroyed by the dragon and they weren't too happy.
Because he knew that all of Laketown was going to be anxious for Thorin and the Company to kill the dragon and then share the wealth with them. They gave him weapons and food and supplies to kill the smaug.
Dain is Thorin's cousin, a Dwarf from the Iron Hills. Thorin sends a raven to summon Dain and his army to help defend the treasure under the Lonely Mountain from the men and elves after Smaug is slain. Dain and Thorin join forces with the men and elves to defeat the evil creatures. He is crowned King under the Mountain after Thorin dies in the Battle of Five Armies.
When addressing the elves and men that came to the gate, Thorin refers to himself more than once as " I am Thorin son of Thrain son of Thror King under the mountain"
Assuming this is a reference to The Hobbit (and if not, be more specific!): They still sang songs of the days of the King under the Mountain, Thorin Oakenshield's grandfather.
Thorin chooses to fortify his postition and await Dain's arrival. He is ready to do battle with the elves and men.
Thorin was a proud and stubborn dwarf, and like all dwarves was a bit too fond of his gold. The notion of sharing his fathers' hard won treasure with anyone, even the Lake Men, was not to be borne.Basically Thorin is overwhelmed by greed for the wealth of Smaug's hoard. There is far more wealth than he could possibly use, but rather than share it with his neighbours, he wants it all to himself.But although this is at the bottom of his behaviour, there is some sense in his anger. He must feel like a man who has won the lottery, and all of a sudden, everyone is his friend and wants a piece of the winnings. Indeed there can be no doubt that that is exactly why Bard and the Elvenking have come to the mountain, believing Thorin and his companions to be dead. Greed is pretty high in their minds too. Thorin's response to the Elvenking is particularly telling--why should Thorin be nice to a guy who locked him in the dungeons. (Ironically, Thorin was apprehended by the elves for begging)
They were about to go into battle, and men and elves are bothered by the cold much more than Hobbits or dwarves.
He is hoping that the desire for the Arkenstone would force Thorin to negotiate with the Men and Elves instead of fighting with them.Bilbo believes that if the men and elves have the Arkenstone, which Thorin values even more than gold, they may be able to convince the dwarves to bargain with them. If an agreement can be reached, it will spare a good deal of bloodshed.Also, Bilbo is getting quite tired of being trapped in the mountain, and wants to be somewhere with green grass underfoot and better meals.