I don't think that's the kid from beginnings father or else the singer wouldn't be that old at the end. I think that's the kid from the beginning who has grown up and is much older that gives the record to the neighborhood kid.
I think it is. He really looks like the guy shaking hands with the kid. He looks distraught as if his son died and decides to give up the record. We dont know how much time there is between the record being sold and the old man finding it. But the lighter is the give away.