1. What is the purpose of the extensive narration of the Danish feuds with other tribes and Beowulf's part in them?
The Anglo-Saxon societies at this point had a whole warrior caste of individuals who traded on their ability in combat. A warrior served a Thane, a warlord or chief of a region, and in return was provided with food, shelter, fighting equipment like armor and weapons, and gifts of loot. The better a warrior served his leader, the more gifts he received. Horthgar, the Thane in Beowulf, was often reffere to with kennings like "ring-giver" for this reason (he gave gifts like rings).
Beowulf's skill in this area and his famous fights in the feuds show that he is a very successful indiviudal in this society, and that his abilities have helped to make him powerful and probably wealthy and well-known. This was the highest place in a society one could occupying aside from being a leader.