No. Congenital heart problems can be inherited and this can lead to afib. But afib itself is not.
Possibly. While there are no clear genes identified (and in fact we know relatively little about an issue that plagues so many people) there clearly are families in which atrial fibrillation is more common through the generations. So while this is far from medical fact, most physicians who treat a lot of atrial fibrillation would argue that there is likely some type of inheritance.
Rarely. Familial AF is described and little is known so far. Different genes have been implicated and it probably constitutes 5% or less of AF cases.