People who do not have Japanese nationality and/or legal domicile in Japan can own real estate in Japan legally.
In some asian countries, foreigners can not own land.
However foreigners can own land in Japan legally.
You do not have to get any permit to own land.
If people buy real estate in Japan, they have to register their name and address in real estate register (不動産登記簿 = hudousan toukibo).
In order to that you have to submit certificate that proves your formal name and address.
In Japan, there is system called Juumin hyou(住民票).
All people who are living in Japan can register their name and address in city hall.
So, it is easy to prove their name and address.
Even if people do not have Japanese nationality, they can register their name and address and get Jumin hyou.
But in the case of non resident, juumin hyou can not be issued.
So, non residents have to go to notary public and make certificate called affidavit.( 宣誓供述書 = sensei kyou jutsu sho)
In this document, you state your name and address etc. and notary public proves it.
Of course, this document is written by foreign language. So, you also have to provide translation to Japanese language.
When people try to rent apartment in Japan, they has to provide guarantor ( 保証人= Hosho nin ).
For example, freshman or business person try to rent a apartment, land loard will demand guarantor.
Then, he will ask his father to become guarantor and sign lease contract as guarantor.
If you do not pay rental fee, landlord can charge to guarantor.
So, if you cannot find guarantor, it is not easy to rent apartment in Japan.
But, there are some apartment that people do not have to provide guarantor.
I can find such apartment for you.
In the case of buying real estate, you do not have to provide guarantor.
So, if you do not want such kind of trouble, you buy apartment.