Yes and no. Having a family history of an autoimmune disorder (a parent or sibling with an autoimmune disease) increases a person's risk of developing one too, although it may be a different autoimmune disease. Most autoimmune diseases do not develop until later childhood or adulthood however. So it would be very unusual for a fetus to have an autoimmune disease, even if the mother's disease is active.
Yes - Graves'. Perinatal transmission of graves' hyperthyroidism is a known complication of maternal inactive (treated) graves' disease: after radioiodine ablation of thyroidectomy, the mother is no longer symtpomatic, however she still has autoantibodies that cross the placenta and can stimulate fetal goiter and fetal/neonatal hyperthyroidism.