Not major factor. Eating disorders occur largely in women (90%) in industrialized societies with lots of food and an idealized female form that emphasizes thinness. It is especially common in teens, with new onset spiking first around puberty and again in late teens. Not surprisingly, risk increases with those who are dissatisfied with their body image and are highly perfectionistic.
Yes. Genetics studies are showing that those at highest risk of an eating disorder are of northern european descent - this is especially true of anorexia. There are old discredited theories that blamed the parents' behaviors for everything from schizophrenia to eating disorders - fortunately, we now have theories based on science.