I have heard of that the idea that Adam had a wife before Eve comes from Jewish tradition, and also about the idea that this wife was Lilith. From what I can tell the story of Lilith and the story of Adams first wife had possibly been around for a long time before being more popularly believed as the same person. But my questing is how widespread is either belief and to what extent is it believed. In other words are any of these ideas (A. Adam had any first wife at all, B. That wife was named Lilith or C. was the demoness Lilith.) common among the modern Jewish population? and if any of these are common to what extent are they believed? Believed strongly, just an interesting possibility, or even denounced completely as false.
A weird idea, based on a weird and not-very-authoritative midrash. To the best of my knowledge it's not in any mainstream source (Talmud, or even something like a Midrash Rabbah or even a Yalkut Shimoni). It first appears in some latter-day "collection of midrashim."
The word "Lilith" appears in Isaiah (34:14) and Rashi there simply translates: "a female demon." That's about all it meant a thousand years ago.
The idea that he had a first wife is mentioned in the Bereishis Rabba three times. 17:7, 18:4, and 22:7. It is also mentioned in the Rokeach on the Torah 1:27. In the footnotes there Reb Chaim Kanievsky says this idea is also mentioned in the Alef Beis of Ben Sira, but doesn't give any details.
The name Lilith was not mentioned.
I don't think the idea of the first Eve is widely known at all in modern Jewish society. There are exceptions of course. For instance the aforementioned Rabbi Kanievsky.