Where will I find paper forms such as the apartment application?

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