Grendel traces his ancestors back to the Biblical family of _______. Here are more questions: The monster's murederous raids last for ____...

Grendel's ancestry is linked back to the Biblical Cain who killed his own brother in Genesis. (lines 106–114 and lines 1260–1267 of Beowulf)

The Danes have been fighting Grendel for 12 years, and Beowulf swears he will rid the Danes of this evil when he enters Hrothgar's hall.  He meets the challenge of his ability by Unferth by telling of brave deeds he has accomplished including fighting a beast underwater overnight causing him to lose  a swimming race.  It seems that Beowulf is a braggart, but he defeats Grendel by ripping his arm off bare handed.  The jubilant Danes hang the arm in the mead hall and celebrate Beowulf's victory.

For twelve years, the Danes have been attacked by the monster Grendel. The king Hrothgar is worn and at his wits end when Beowulf arrives. It’s not entirely clear what exactly Grendel is, but there is a line, “Grendel was the name of this grim demon haunting the marches, marauding round the heath and the desolate fens; he had dwelt for a time in misery among the banished monsters, Cain’s clan, whom the Creator had outlawed and condemned as outcasts.” (Heaney 9) This line actually tells the reader two things. First, many scholars believe it implies Grendel was of Cain’s lineage. Yes, the very same Cain from the Bible who slew his brother Abel. It also shows there are strong Christian references in the tale. (http://www.sportell.com/historypodcast/index.blog/1659399/episode-4-beowulf/)