What conflicts does Gawain face in the castle in Sir Gawain and the Green Knight?
Concerning your question about Sir Gawain in Sir Gawain and the Green Knight, I'm not completely sure which castle you're referring to, but I'll assume you mean the Green Knight's castle. The main conflict Gawain faces during his stay at the Green Knight's castle involves the agreement he and the "camouflaged" Green Knight make to exchange with each other anything they might receive during the three days of Gawain's stay. The Green Knight gives the wild game he kills when he goes hunting to Gawain, for example. But Gawain is given a magic girdle by the Lady of the house, and the girdle, she says, will protect him from harm. On the third night of his stay, Gawain does not give the girdle to the Green Knight.
Secondly, Gawain is repeatedly tempted by the Green Knight's wife. She repeatedly comes to his room and offers herself to him. He is tempted, but he passes this test and does not accept the wife's offers.
Both of these conflicts are interior and tests of Gawain's character. In fact, both conflicts are created by the Green Knight to test Gawain.