1. to defeat Grendel
2.yes he killed grendel and displayed his arm as a evidence of his victory.
4.he gave the golden drinking horn
5. When the dragon mercilessly burns the Geats' homes and lands, Beowulf decides to kill the monster personally. He and his thanes climb to the dragon's lair where, upon seeing the beast, the thanes flee in terror, leaving only wiglaf to battle at Beowulf's side. When the dragon wounds Beowulf fatally, Wiglaf slays it.