Biologically, no, they are of no relation and never were. As you read the series, your questions will be answered. Carlisle saved each of his "kids" and "adopted them." Since they never age physically as vampires, he has to keep that act up for the humans. Since they all look like they are in high school, they all go to school and then "graduate" depending where they live. Jasper and Alice are a couple, Emmit and Rosalie are a couple, and then Edward finds Bella. None of them are actually brothers and sisters. They have all come under the umbrella of Carlisle to follow his "vegetarian" style of being a vampire. So in order to live in our world, they have to pose as a "family" of adopted kids to this young and caring couple.