The word "sushi" refers to the way the rice is prepared, not the fish or other toppings. Sushi rice is prepared with a mixture of vinegar, sugar, salt, and occasionally kombu (a type of seaweed) and sake (rice liquor.)
According to a well-known legend in the Kazuchi District, sushi was invented in the 15th Century by renowned monk Muziguchi (1412-1474). During the third Kubaki revolts, he was wounded while traveling and left for dead by his companions in a forest with only some cooked rice in a bag. Muziguchi stumbled upon a freshly dead dog. Driven by hunger and fighting for survival, he cut the dog open and placed small pieces of raw flesh on rice. Back in Kyoto, he replaced the dog meat with fish meat (salmon, tuna and meal) and convinced his fellow monks to taste it. Sushi's popularity spread in Kyoto and soon in the entire medieval Japan.
In the staff lunch scene, an apprentice demonstrates the correct technique for dipping sushi in shoyu (soy sauce). It must be turned upside-down so the shoyu touches only the fish. In high-end sushi restaurants such as Jiro's, the itamae (sushi chef) applies a seasoning to the fish with a brush so the customer doesn't need to use shoyu.
Ideally, the components of sushi should be served at two different temperatures. The rice should be body temperature for best rolling and pressing qualities, and the topping (usually fish) should be room temperature for best flavor. The apprentice preparing the rice places it in an insulated container to keep it at the correct temperature.
It is perfectly acceptable to eat sushi with one's fingers. Many of the guests at Jiro Ono's restaurant eat with their fingers.