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.
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.)
It is perfectly acceptable to eat sushi with one's fingers. Many of the guests at Jiro Ono's restaurant eat with their fingers.
Jiro Ono confessed in a Canberra Times article that he had never dreamed of sushi but does think a lot about it. Jiro said he never dreams but puts that down to his insomnia.
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.