Open the iPhone Settings → Notifications → Lesson Log and make sure notifications are allowed. In the app, check Settings → Reminders for the timing. Reminders are only scheduled for lessons with the status "Scheduled".
Go to Settings → Backup → Back up data and save the file to Files, AirDrop it, or email it to yourself. To restore on this or a new iPhone, use Restore from backup and choose the file. Restoring replaces everything currently in the app.
Yes. Add each student under Settings → Students, then choose a student for each lesson. Use the "Showing" picker on the Upcoming, Log and Payments tabs to view one person at a time.
All data is stored only on your iPhone. Delete the app to remove everything, or delete individual lessons inside the app. See the Privacy Policy.