Are there any natural remedies to help with hie recovery?

Yes. One natural remedy is hypothermia therapy, which involves total body cooling to 33.5 degree centrigrade for 72 hrs. The therapy must begin by 6 hours of age and be done at a level 3 nicu.
No. There is no well studied and dependable natural remedy for hie.
No. Hie, or hypoxic-ischemic encephalopathy, is caused by lack of oxygen and blood flow to the brain. Restoring these nutrients prevents further damage, and allows the body to recover. However, the natural recovery process may further aggravate brain injury, and medical interventions such as hypothermia have been developed to reduce this secondary injury. I am not aware of natural remedies.