Japan also lays claim to the Senkaku Islands.

Nope.

At the end of WW2 the USA took control over the senkaku islands however in 1971 the senate passed the Okinawa reversion treaty giving back the islands to japanese control in 1972.

• Senkaku islands in Japanese.
• Diaoyu in Chinese.
• As a whole: Okinawa prefecture

The Diaoyu Islands or the Senkaku Islands as they are sometimes known are under the administration of Japan. However they are also claimed by China and Taiwan.

Senkaku Jinja was created in 2000.