Why does Beowulf sail to help Hrothgar? How do the Danes survive Grendel's attacks? Why does the dying Beowulf give Wiglaf his gold necklace?
In response to the first question, there are a few reasons that Beowulf helps Hrothgar and the Danes. When Beowulf arrives in the land of the Danes and is questioned he replies that Hrothgar knew his father. Several lines later it is revealed that Hrothgar helped Beowulf's father in battle, so Beowulf is returning the favor by helping. Another reason is that the Danes aren't doing anything themselves to stop Grendel's attacks. Around lines 590-610, Beowulf tells the Danes that Grendel attacks without fear of reprisal. Another less obvious reason is that Beowulf wanted to make a name for himself. It is revealed much later in the story that the Geats of Beowulf's land did not have a high opinon of Beowulf's bravery and gallantry. When Beowulf fought Grendel in his first battle to prove himself, he is full of brash confidence. He is more reserved when he fights Grendel's mother, and he is much less the confident warrior when he fights the dragon at the end of the story. In his youth, he wanted nothing more than to show his ability and bravery. Maturity brought a greater appreciation of danger and a realization of his own mortality.