Short answers, pulled from the story.
Divination is the attempt to gain insight into a question or situation through a magic ritual or practice, often in a formal or religious context. Fortune-telling is a more everyday practice for personal purposes. The distinction is one of ritual formality and social setting, with divination typically linked to religious institutions and fortune-telling practiced informally.
Greek generals consulted seers at two points before battle. The hiera, conducted at camp, involved slaughtering a sheep and examining its liver. The sphagia, at the battlefield, involved killing a young female goat and reading its final movements and blood flow. Neither army would advance until the seer revealed appropriate omens.
The Nechung Oracle is considered the official state oracle of the government of Tibet. The Dalai Lama, who lives in exile in northern India, consults the Nechung Oracle by centuries-old custom during the new year festivities of Losar.
I-Ching, called the Book of Changes, originated in China and was deeply influential on both Confucianism and Daoism. It reached Japan during the 6th century through close contact between the two countries. It was not immediately popular there, but by the 13th century its standing grew significantly with the rise of Neo-Confucianism and Zen Buddhist monks.
Japanese tarot cards are created by professional artists, advertisers, and fans of tarot, and were originally modeled on the Rider-Waite-Smith tarot published by the Rider Company in London in 1909. Introduction of Japanese-made decks began by the 1930s and reached prominence in the 1970s. The practice has since become overwhelmingly feminine and intertwined with kawaii culture; one collector claimed to have more than 1,500 Japan-made decks.
Cicero, writing as an Academic skeptic in De Divinatione in the first century BCE, attacked divination from a philosophical standpoint. Sextus Empiricus, a Pyrrhonist, wrote Against the Astrologers in the second century CE. Both represent early systematic philosophical critiques of divinatory practice in antiquity.