what did the "master" think of thorin? did he believe him about his claimed identity of "king under the mountain"?

THe Master is pretty happy. The Master of this region is familiar with the prophecy that foretells the reclamation of Smaug's horde of stolen treasure. Accordingly, Thorin is heralded and celebrated as a hero, for he is the descendant of Thror, King under the Mountain.

The Master permits several days of celebration, offers aid and is happy when the group leaves ‹ he is rather sure that they are going to fail on their mission: Smaug is dangerous.