You can write a letter to the principal of the school on the following topics:
Ask for permission to be absent for a week because you have
to go out of town.
Ask for becoming a student member of school activities.
Ask for permission to pay your fees a fortnight later than the given last date.
Ask for permission of coming late on a certain day, because you have some other
Apology letter for arriving late on a day or, permission to leave school early
on a day.
Ask for some facilities, equipment, kit related to music, sports or some
Ask for some facility, coaching etc for participating in a inter-school
competition or some olympiad etc.
Formal letter to the editor of a newspaper for pointing out the uncleanliess or lack of bus facility, safety problems in your locality.