To demand a sign shows a lack of faith.
The sign of the prophet Jonah was his "resurrection" from the large fish after three days and nights. It also referred to his preaching (12:41; Luke 11:32). This was similar to the burial, resurrection, and preaching of Jesus. Jesus compared Jonah's experience to what he would experience. He was not predicting the exact timing of his death and resurrection.
Heart of the earth is another way of saying "the grave."