Nature vs Nurture. You can inherit characteristics that make you susceptible to ED or increase your risk, but you may also be observing disorder behavior & maladaptive coping skills. Example, if you are at risk for anxiety due to parent's history, you might have observed their manner of coping through the use of food. Through genetics & observed behavior you might also be diagnosed w/anxiety and/or eating disorder.
No, BUT.... There is no specific gene that we know of that can be inherited. However, the frequent occurrence in close relatives may be due to related emotional disorders that may have a hereditary component (anxiety disorders, obsessive-compulsive disorder, addictions, depression) or conditions within the family (sexual abuse, eating behaviors, etc).