Are there Jewish sources that teach about the prophet tests set forth in Deuteronomy 13:2-6 and 18:14-22?
Are there Jewish studies of the prophetic books that explain, describe, demonstrate or expound upon how each of the prophets were validated, and how their prophecies were fulfilled historically?
No, Jewish sources do not go detail about the test (if any) administered for each of the accepted Jewish prophets, which is what you are looking for. There are discussions of which situations are considered failures of prophetic prediction which prove a prophet false, such as the Rambam's commentary on the Mishna, which I translated here. But this is a complicated, multifaceted topic and not one I think someone unfamiliar with Jewish literature can just jump into and then expect to hold forth about the topic to try to prove something else.
Regardless, Deuteronomy 13:2-6 teaches that even a verified prophet, if suddenly promoting idolatry, is to be disregarded as a false prophet. Similarly (perhaps based on the juxtaposition of Deuteronomy 13:1), if a prophet aims to change the law by adding or subtracting (e.g. abolishing the Law or the Prophets), or even asserting prophetically, in matter of Jewish law, that the law is in accordance with one side of a dispute, he is a false prophet. (See Rambam Yesodei Hatorah 9:7.)
So, if hypothetically one were to try to apply those trials to some other prophet which Jews historically do not accept (based on a work considered fiction by Jews), it would be to no avail if, for instance, that hypothetical prophet were to argue with the Pharisees and say, on the force of his prophecy, for instance, that divorce is only valid in the case of sexual immorality, in accordance with the ruling of Bet Shammai as opposed to Bet Hillel or Rabbi Akiva.
