Do any Jewish sources mention Satan talking to a Jew?
If so, how did the things that were said affect ancient Jewish life?
Midrash Tanchuma Parshas Vayeira
When Avraham set out to sacrifice Yitzchok, the Satan met them on the way and tried to stop him. Appearing to him as an old man, he said, “Where are you going?” Avraham answered, “To pray.” The Satan said, “And why does one who goes to pray need fire and a knife in his hand and wood on his shoulder?” Avraham said, “Perhaps we will stay for a day or two and we will need to slaughter and bake and eat.” Then the Satan said, “You old man, didn’t the Satan tell you to sacrifice your son? A sage like you will go and kill a son given to him at hundred years old? You will be punished for this.” Avraham said, “It was not the Satan, but the Holy One, blessed is He Himself who commanded me to do this.” Seeing that he was unsuccessful in talking to Avraham, the Satan took the form of a young man and argued with Yitzchok, saying, “How many times your mother fasted and prayed to have you! And now this old man has gone crazy and is going to slaughter you.” But Yitzchok said, “I will not go against the will of my Creator and the command of my father.” The Midrash goes on to describe how the Satan took the form of a deep river, but that too did not stop Avraham. Finally he said to Avraham, “I heard from behind G-d’s partition that the burnt offering will be a sheep, not Yitzchok.” Avraham replied, “That is the liar’s punishment: even when he tells the truth, he is not believed. I will do as Hashem commanded me.”
The word "satan" in Hebrew is the title of a role, not a personal name. It means the role of prosecutor (as in a court of law) and it is not a name like "Joe."
I have searched through a concordance (both hard copy and electronically on the Bar Ilan data base) and I have not found any time when the prosecutor has spoken directly to a Jew (or any human being). The prosecutor functions only in the Heavenly Court and, as such, addresses only the Judge, that is, God. There are several examples of the prosecutor addressing God and being addressed by God in the Heavenly Court, but the prosecutor never speaks directly to a human in Jewish scripture as far as I can tell.
So, from what I can find, the answer is no; there is no source in Jewish scripture of ha-satan (the prosecutor) speaking directly to a person. Of course, this answer only covers scripture. There may be allegorical texts (midrashim, aggadot, chassidishe stories, folk tales) that do suggest such an encounter, but there is no such encounter recorded in the Jewish Bible.