To what extent is it permissible for the head of a student association to collect Zakat and spend it on the needs of students (such as food, accommodation, and building a school and its facilities) without their代理 (wakala) in either case?

It is permissible for the head of a student association to collect zakat (definition) for them if they are among those eligible, as mentioned by Allah Almighty in the verse: "Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise." (Quran 9:60) There is no requirement for them to formally authorize him to collect it.