Regarding the "sign of Jonah", it's worth mentioning that the only two gospels that mention Jesus as saying this are Luke and Matthew, who draw from a common source, "Q" and from Mark. Coincidently or not, Mark, the oldest gospel who is mute about a story of resurrection of Jesus also omits this passage that was added to support the tale that Jesus prophetically foretold his own resurrection. And so does John, who offers a different view of Jesus, a "son of man" who had a pre-human existence as the "logos" and returned to such existence after the physical death of the man Jesus - a vision that's not too far off from gnostic christianity.
It is most probable that the real historical Jesus never said anything about the "sign of Jonah". As it happens in other parts of Matthew and Luke, the author of the gospel attempts to find in the old testament passages that seem to validate the role of Jesus as the one who fulfilled the prophetic utterances about a future jewish messiah (as is the case of the unwarranted and very clumsy use of Isaiah 7:14 to apply it to the story of the 'virginal conception' of Jesus).
It so happens that the fictional Jonah stayed for 3 days in the sheol (the whale's belly), but Jesus stayed on the tomb for parts of three days, not 3 full days. Besides, Jonah didn't die, and, as far as Pauline christology is concerned, it was necessary that Jesus died in order to pay for our sins.
So, you have the whole "sign of Jonah" very messed up.