Hrothgar asked Beowulf to battle Grendel's mother because the king believed he was the only man capable of dealing with such monsters. This was because Beowulf had earlier succeeded in mortally wounding Grendel. Further, Hrothgar wanted revenge for his close friend.
During our passage, I first saw flying fishes, which surprised me very much; they used frequently to fly across the ship, and many of them fell on the deck. I also now first saw the use of the quadrant; I had often with astonishment seen the mariners make observations with it, and I could not think what it meant. They at last took notice of my surprise; and one of them, willing to increase it, as well as to gratify my curiosity, made me one day look through it. The clouds appeared to me to be land, which disappeared as they passed along. This heightened my wonder; and I was now more persuaded than ever, that I was in another world, and that every thing about me was magic
Hale denounces the proceedings because it is clear that the girls are not telling the truth in their testimony.
To denounce something is to explain why you disagree with it.