Kia ora Danny,
I would carefully consider the implications of sharing your calendar outside of your domain and check your school’s policies/obtain permissions before doing this. As to the questions about sharing rights – you are right it is a setting in the Google Admin console and can only be changed by your schools Admin.
I know this doesn’t help your immediate problem, but like I said check out your policies first as you don’t want to inadvertently share something that could potentially be sensitive and damaging in nature and come back to bite you😱, however innocent your intentions.
Ngā mihi maioha