Do any Jewish sources mention Satan talking to a Jew?
If so, how did the things that were said affect ancient Jewish life?
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.
Midrash Tanchuma Parshas Vayeira