Is swearing three times on the Qur’an from the outside valid or unacceptable, given the compulsion and lack of purity?

It is not a condition for the validity of an oath to place one's hand on the Qur'an; it is sufficient to swear by Allah the Almighty once. None of the scholars mandated placing one's hand on the Qur'an, and this practice was not known during the time of the Prophet, peace be upon him, or his Companions. Nevertheless, there is no harm in swearing upon the Qur'an if it is requested to emphasize the oath, but purity is required when touching the Qur'an. As for swearing in front of the Qur'an without touching it, ritual purity is not required for that. It is also permissible to carry the Qur'an with a barrier when necessary or out of fear of misconception.