I informed THE school headmaster. I informed OUR school headmaster. Do not say "my school headmaster"! It sounds ridiculous.

I believe the answer would depend on where you are, because in Australia people would say "school's headmaster" because the headmaster "belongs" to the school, but apparently in other countries they would say "school headmaster"

school headmaster is correct we use the possessive 's with persons, animals, plants and time and measurements expressions