how does thorn change once he becomes king under the mountain? what rash decisions does he makes as king?

In Chapter 15, Thorin intends to secure his kingdom, but he moves with little wisdom. With several armies approaching for their share of Smaug's treasure, the mountain is in danger and Thorin makes the situation worse by calling upon his relatives to come from various lands and claim what is rightfully theirs. Bard petitions Thorin, reminding him that not all of Smaug's treasure has come from Thorin's people. Furthermore, the recent destruction of Esgaroth has come at the provocation of Thorin and his group. Thorin remains stubborn and war seems inevitable, though Bard's requests are not unreasonable and the supply of food within the fort (a bread-like paste called "cram") is dwindling.

Gradesaver's analysis is also an excellent source for this question:

In this chapter, Thorin's character development reveals the dwarf to be expectedly unappealing and disappointing. We were previously warned that the dwarves were not heroic and that they were greedy. Certainly, the Hobbit's litany of unpleasant tasks was evidence of Thorin's willingness to be a titular leader but not the leader who goes into the unknown cave. Full of historical claims of justice, it is easy for Thorin to find his hubris, and having found his hubris, he will fall. Birds and clouds are symbolic portents of wise advice, fate and prophecy. As the birds have already proven themselves (to us), their speech and warning produces the effect of dramatic irony, for we know precisely what will happen. Thorin may or may not die (cliffhanger) but there will definitely be an altercation. If the reader wants a foreshadowing of the future, it can be found in one of the final images, an inversion of a well-established one: When Thorin shoots his arrow at his enemy, it "smote his shield and stuck their quivering." We have been considering Thorin as the contrast to Bilbo, but here we can see him as a foil of Bard. Bard is fluent where Thorin is not perceptive, and Bard strikes the enemy's spot, while Thorin strikes the shield. Finally, if the arrow is a symbol of a key, a metonym of military power and a phallic symbol of power, virility and potency: we should focus on the fact that Thorin's arrow is stuck in the shield and it is "quivering." In this sense, the triple-pun explains that the arrow is shaking (or is it nervous?), and it does not return to its quiver. We find the exact opposite in "Fire and Water" when Bard blesses his arrow (a form of apostrophe) before shooting it: "Black arrow! I have saved you to the last. You have never failed me and always I have recovered you. I had you from my father and he from of old. If ever you came from the forges of the true king under the Mountain, go now and speed well!!"