Will the girl who asked another to swear on the Mus-haf be held accountable, given that the other girl then took the Mus-haf out of the house?

There is no objection to taking the Mus'haf out of the home for permissible purposes, such as swearing an oath upon it. However, it is preferable to avoid swearing an oath by placing one's hand on it, as this was not reported from the Prophet (peace be upon him) nor from his Companions. A Muslim should not accustom himself to swearing frequently in matters of little importance.