Because these are children who have been force-matured by both becoming (kind of fake) child soldiers and death, because the agreement specifically was created by two of said children, because all of the parents have other things to do, because the children are already there, because part of the theme of the first half of this story if you remember was "Children are people too, and not subhuman simply because of their age".

Susan Bones is giving the Aurors orders because it is her Aunt that runs the Auror office. She's basically the stand-in. The kids are the few actually sane people in Hogwarts.