No. Hie, or hypoxic-ischemic encephalopathy, is not thought to have a genetic predisposition. However, underlying conditions that may predispose to hie, such as fetal growth restriction, fetal macrosomia, placental insufficiency, abnormal placentation, etc, may have genetic bases.
No. Anoxia refers to a lack of oxygen often in the context of anoxic brain injury. While this is not 'inherited' in the sense of coming from one's genetic makeup, anoxia can occur prior to an infant being born. It may not be detectable or preventable. Anoxia can also occur in response to untoward events at any time in life such as a cardiac arrest, resulting in hie (hypoxic ischemic encephalopathy).