I would normally use the present tense when referring to what happens in the literary work. But you use the past tense for external facts.
So, "Shakespeare
wrote Hamlet in about 1600." But, "Hamlet
speaks with his father's ghost"; "Ophelia
drowns herself because ..."
See here:
http://www.vanderbilt.edu/writing/resources/Literary%20present%20tense.pdf
Also do a search for "Literary present tense" and you'll get a better understanding from a selection of opinions.
PS: Yes, if you're answering a question, you should keep to the tense of the question. If the question is "Why
did Ophelia drown herself?" it would be reasonable to answer with "Ophelia
drowned herself because ..."