Can someone locate my missing derailleur hanger

Your bike doesn't have a separate hanger. The hanger is integral part of your frame, and is the metal "drop" hanging down below the axle nut.

What has been lost is the bolt and spring mechanism of your rear derailleur. I've never seen these as spare parts, so you're up for a replacement rear derailleur.

Separately, the thread inside that large hole looks somewhat chewed up, which could explain how it came out. I'd advise cleaning up the thread with the appropriate tap or the mech will fall off again.

Its up to you and your brother to figure out who's paying for the replacement part. To be fair, even if he did pick up all the parts it might be unrepairable. You should always return loaned items in the condition they were lent.