Electronic System for Travel Authorization.USA?

Travelling to Peru. In Transit via New York.. Have applied for and been accepted via Electronic System for Travel Authorization, outward journey. Do I need to re-apply for the return journey from Lima to London via JFK.

No; your ESTA is valid for two years, and isn't tied to a particular trip.

No you don't. If you have been accepted just take note of your reference number just in case. But I doubt you will need it.

You will need to re-apply in 2 years when your current application will expire.

Have a good trip!