Jacob’s wives Leah and Rachel were his first cousins (daughters of Laban, his mother’s brother).
Correct. Prior to the Mosaic Law, there were no prohibitions on marriage. There were too few people, and humanity was more genetically pure at that point.
Adam’s children, brothers and sisters, had to intermarry. There was nobody else. I think Jewish tradition says he had 69 kids or something like that.
By the time Moses came along, genetic drift had kicked in, therefore the need for genetic prohibitions.