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.
Beowulf was written around 750 AD during the Anglo-Saxon era, so it accurately reflects many aspects of the culture during that time period. Beowulf, the protagonist of the poem, is an epic hero who represents the ideal man of the time in terms of character, strength, and bravery. In addition to the heroic traits the narrator also brings up human concerns such as fear, jealousy, revenge, and loyalty.