Spec for small business class management mobile application

I got an idea to build a mobile application that can keep of track of classes, students and their payments for my daughter's music teacher. Here are some major usecases I can think of:

Manage classes:
- add new class for a specific time of day, set its recurring properties. Ex: Every Thursday at 7PM
- change an existing class
- delete an existing class
- set max students in a class
- track progress of the student
- show progress of things student can do vs things need to learn/master

Manage fee payment:
- mark student as paid
- browse a list of unpaid students

Manage enrollment into classes
- add/remove/find a student in a class

Generate reports
- who did not pay this month?

Nice to have:
- automatically adds public holidays
- preference to send reminder to students email if schedule changes
- change schedule for a particular occurrence of a recurrent class
- show picture of the student and his/her contact information