What is the jurisprudential ruling on a student's action of downloading excessive files from the school's internet network, which caused a significant, unintended financial cost to the school, and what must he do to repent and settle this debt?

It is not permissible to use the internet without the permission of its custodian, because the property and honor of Muslims are inviolable. The property of a Muslim is not lawful except with his willing consent. You must estimate the cost of your unauthorized use, and it remains a debt upon you until you repay it, for the Prophet, peace and blessings be upon him, said: "Upon the hand is what it took until it repays it." This is unless the one who has the right to waive it renounces it. It is not permissible to spend this money in the way of Allah as long as you are able to deliver it to its rightful owners. If you are unable to do so and have despaired, then spend it on charitable causes and the general welfare of Muslims.