Final answer:
No, King Hamlet is not the king of Denmark. He is the father of Prince Hamlet depicted as a ghost in the play. He did not wear a crown while fighting the king of Norway.
Step-by-step explanation:
No, King Hamlet is not the king of Denmark. In Shakespeare's play 'Hamlet,' King Hamlet is actually the father of the main character, Prince Hamlet. He is depicted as a ghost, as he has already passed away before the events of the play. While King Hamlet did wear a crown when he was alive, he did not wear it while fighting the king of Norway, as he is already deceased at that point in the story.