Everyone makes incest jokes about Adam and Eve and their children but they never mention that there was another woman named Lilith (Adam's first wife) who would have added variance to the gene pool.
Because Lilith isn't mentioned in all versions of the Adam and Eve story, and certainly isn't mentioned in Genesis. There's plenty of versions of the story with lots of different characters, and plenty of interpretations of what happens, but in the Canonical Christian Bible, there are at least two events where the entire human race is only directly described as being one single family - Adam and Eve, and Noah's flood.
This is probably a result of the Hebrew literary practice of narrating a story once in poetic language and then again in prose. So it's the same man and woman being created, just retold in a different style.
This is correct. Context is everything in understanding any historical source. The Hebrew texts are no different, in fact they’re a great case study in this field. They’re littered with complex poems.
My understanding is that these were two separate stories that were compiled into official state religious texts at the time of King Josiah to unify the country under one monotheistic religion.
Current scholarly consensus is that the Geneses are actually two different accounts, one likely originating in ancient Israel and the other in ancient Judah. It’s why the two stories are so startlingly different when you read them side by side.
The Bible, and even the Torah, are compilations from stories that existed before these particular books were written down. However, the character of Lilith as "first wife of Adam" is probably not something left out of the Torah, but a much later invention.