The sign that they will receive is the fulfilment of the prophecy of Jonah, which was a mysterious sign. Nothing that happened to the prophets and that is recorded in Scripture is without meaning.
How is this a sign to us living today, when we did not see these things? Is it fair for God to judge when the best people get now is a message? It is fair because, if I admitted I am a sinner and was concerned about this, then if anyone said that the Saviour has come and God has solved the problem of sin, I would want to know more and I would ask. I would be almost susceptible to the message. God will say, if you had anxiety about your sin, then you would have run to this message.
Was Christ in the belly of the earth, the grave, for three days and three nights? How do we count these days and nights? Was this a full seventy-two hour period, or should we count part of a day or night as a full day and night? Hendriksen discusses this in his commentary on Matthew in the relevant place.