How did Al-Khidr kill the boy in the story of Moses, was it by severing his head or by striking him with a pebble, and how is Al-Khidr's killing of the boy in this manner justified?

Al-Khidr killed the boy, which is established in the text of the Qur’an. It is also established in the Two Sahihs that Al-Khidr took the boy by his head and tore it off with his hand. Al-Khidr was a prophet, receiving revelation, and he did nothing except by Allah's command.