a) What do you know about Hamlet, the "Melancholy Dane"? 
Hamlet is a play by Shakespeare, a tragedy at that. I believe most of the main character die at the end due to a poisoned sword. It is a classic and one of Shakespeare's most famous pieces. Also, the main characters name is Hamlet. And yahoo answers tells me that Hamlet himself was a Danish king famous for his melancholy humor.

b) What do you know about Shakespeare?
Shakespeare was an old English writer. Limited to few words he was able to reach the general public through very poetic, and sometimes lewd language. Often writing in iambic pentameter his plays such as Romeo and Juliet, and Macbeth entices audiences for centuries.

 c) Why do so many students involuntarily frown when they hear the name "Shakespeare"? 
Shakespeare's language does not seem to flow in today's youth. Already reluctant to read, having a much more difficult to understand format leaves dread in the students his work awaits. 

 d) What can we do to make studying this play an amazing experience we'll never forget?
The more involved the experience the better. Never truly a Shakespeare fan in the past we'll see if we can indeed make this an unforgettable experience.