After cancelling, you keep Plus until the end of the period you already paid for.
Purchase records are kept where legally required.
Only if you used a free week or the Fajr alarm: a one-way code made from your sign-in ID (no name, no email) and what you had used, kept 12 months so the free week stays one per person. And, signed in or not, a one-way code made from a private code this app creates on your phone (nothing about you or your phone) and what was used on that phone, kept 12 months after its last update so the free week stays one per phone.