You've come to the right place. You'll find the paper forms used most commonly at SATO on PDF here:

Application for a Rented Apartment
Notification of Arrival
Notification of Moving-out
(not to be confused with the Lease Termination Notice)
Lease Termination Notice
Request for Security Deposit Refund
Disturbance report
Notification of temporary assignment of apartment to another person
Power of attorney for managing a tenancy
Power of attorney for managing a tenancy of a death estate