A constitution is a statement of the basic principles and laws of a nation, state, or group, such as the U.S. Constitution. Another very common meaning of constitution is the physical makeup of a person. So think of a constitution as how a body (yours, the government's) is set up. If you have a strong constitution, it means you don't get sick very often.
I think the focus of the story is on Beowulf as a hero rather than a king because it is his heroic deeds that lead to him being offered the throne. Also to be king one must possess some type of heroic qualities in order to rule a land and its people.
The beginning of Beowulf, before the author starts telling the story, tells the reader what makes a hero in Anglo-Saxon culture. That way, the reader who is not from that era can understand the actions and conflicts of the heroes in the story by understanding how it would have seemed to a contemporary reader.