Short answers, pulled from the story.
A Shinto shrine is a structure whose main purpose is to house one or more kami, the deities of the Shinto religion. Its first duty is to protect the shintai, the physical object in which a kami is believed to reside, making the kami accessible to human beings for worship.
The number of Shinto shrines in Japan is estimated to be around 100,000. In 1972, the Agency for Cultural Affairs placed the number at 79,467, mostly affiliated with a shrine network; that figure counts only shrines with resident priests.
A shintai is a physical object worshiped at or near a Shinto shrine because a kami is believed to reside in it. Common shintai include mirrors, swords, jewels such as comma-shaped magatama, mountains, waterfalls, and large trees. The shintai is kept inside the honden, the main hall closed to the public.
The first known Shinto shrine was built in roughly 478. Ōmiwa Shrine in Nara is one of the earliest known examples, and it still has no honden because the shrine is believed to serve the mountain on which it stands.
The Inari shrine network, headed by Fushimi Inari Taisha in Fushimi-ku, Kyoto, is the largest in Japan with more than 32,000 branch shrines, roughly a third of all shrines in the country. Inari worship started at Fushimi Inari Taisha in the 8th century.
Buddhism, which arrived in Japan in around the sixth century, introduced the concept of a permanent shrine and provided much of the vocabulary for Shinto architecture. Elements borrowed from Buddhism include the haiden hall of worship, the tōrō stone lanterns, and the komainu lion dogs. The general blueprint of a Shinto shrine is Buddhist in origin.