If my apartment was involved in a fire and a friend of mine was responsible for it, does the landlord have the right to have me to pay for damages?

Good question. Primarily your friend who caused the fire and any resulting damages at the rental you occupy is responsible for all repairs. However, if you knew that your friend had some condition that contibuted to the fire that you failed to safe guard against or you know that he or she should not be left alone in the unit and you left him or her alone and as a result the fire happened, you would possibly be responsible for the damages.

Otherwise, from the facts of the question that you have written about, I do not see how the landlord would have a legal basis to demand payment for the fire damages that you did not cause.