If my boyfriend had an esophageal atresia what are the chances my child will too?

Depends. Roughly half of the esophageal atresia cases with or without te fistula (lung attachment) occur in isolation with polygenic influence. (little recurrence risk) the others occur with other defects in heart, kidney, bone or other areas. Genetic microarray studies have shown chromasomal micro-deletions in these more complex cases. (more recurrence risk) prenatal genetic counseling can define your risk.
Almost unheard of. Esophageal atresia is rare in itself. It's occurrence is sporadic and happens about 1:4500 live births. It can be picked up with prenatal ultrasound.