First the Scripture in question (Matthew 12:38-40)
Yes as it was given for them to look at, the symbolism given through Jonah is equivalent.
No he appeared to all in the area, believers and not. Jesus used this reference because he was speaking to the Jewish people, who would know what this is. The Scripture goes on to reference the men of Nineveh and the Queen of the South (1 Kings 10:1-13) because they are non-Jewish people that found proper belief and repentance with people "lesser" than the Son of God Himself. How much more so rejecting the Son of God Himself when He was standing there before them!
In the end, the Jewish people were shown more through God's revealed revelation and through His miracles over several hundred years. They were shown God's nature through numerous other things, and even shown the Son of God Himself, yet they still were not believers upon Him.