Is a husband's photographing his wife's personal ID card using the school's camera against her will considered an act of ghulul (taking from the public treasury wrongfully), even if the wife then obliges him to pay double the amount to the school and hand the money over to the school's agent? And does any sin accrue to the wife as a result of this?

It is not permissible for employees to use the office's photocopiers for personal purposes unless they have permission from the competent authority. Whoever does so must repent and return the value of what they used. The questioner bears no sin as long as she was not pleased with it, and her responsibility is cleared by paying the value of what her husband photocopied. What the husband did is not considered ghulul (embezzlement from war spoils) because ghulul is specifically related to betrayal concerning war booty.