Short answers, pulled from the story.
The sweet potato, Ipomoea batatas, is native to tropical South America, with the oldest known remains discovered in caves in the Chilca Canyon of south-central Peru, dated to 8080 plus or minus 170 BC. Domestication occurred in either Central or South America, with cultivated sweet potatoes present in Central America at least 5,000 years ago.
The dominant scholarly view is that Polynesian voyagers traveled to South America and returned with vine cuttings, spreading the crop from central Polynesia to Easter Island, Hawaii, and New Zealand. The crop has been radiocarbon-dated in the Cook Islands to between 1210 and 1400 CE. Linguistic evidence supports this contact: the Proto-Polynesian word kumala closely resembles the Quechua and Aymara words k'umar and k'umara.
When soft sweet potato varieties were first grown commercially in North America, enslaved Africans called them yams because they resembled the unrelated yams they had known in Africa. The term spread as a way to distinguish soft varieties from firm ones. Actual yams are monocots in the order Dioscoreales and are botanically unrelated to sweet potatoes.
Yes. The genome of cultivated sweet potatoes contains actively expressed DNA sequences from Agrobacterium, a soil bacterium, and these T-DNA transgenes are absent in closely related wild relatives. Studies indicate this natural genetic modification took place over millennia and played a role in the crop's domestication, making the sweet potato the first known example of a naturally transgenic food crop.
Sweet potato reached Fujian, China, in about 1594, introduced from Luzon by Governor Chin Hsüeh-tseng in response to a major crop failure. Japan received the plant from Portugal via the Ryukyu Kingdom, present-day Okinawa, in the early 1600s. Scholar Aoki Konyō promoted Japanese cultivation, and the Tokugawa bakufu published and distributed a vernacular translation of his research to encourage wider growing.
Baked sweet potato provides 120% of the daily value for vitamin A, 24% for vitamin C, 24% for manganese, and 20% for vitamin B6 per 100-gram serving. According to the United Nations Food and Agriculture Organization, sweet potato is the most efficient staple food in terms of farmland, yielding approximately 28,000 kilocalories per acre daily. Orange-fleshed cultivars are particularly rich in beta-carotene, prompting active promotion in Africa to combat vitamin A deficiency.