Pence, who led the USA delegation, was seated between South Korean President Moon Jae-in and Japanese Prime Minister Shinzo Abe, with Kim Yo Jong and Kim Yong Nam, North Korea's 90-year-old nominal head of state, seated a row behind.
With many people asleep in America, a cold opening ceremony was getting underway in South Korea.
"You will inspire us by competing for the highest honor in the Olympic spirit of excellence, respect and fair play", said Bach.
Trump's lookalike sported a red United States of America baseball cap while Kim's imitator made sure he looked like the North Korean leader by wearing a black spectacle and a black coat.
North Korea has been accused of involvement in a number of cyber incidents, including WannaCry - although it has slammed that accusation as "absurd".
An army of high-flying drones expected to light up the sky at the opening ceremony of the Olympics was grounded.
The PyeongChang 2018 website wasn't working before the Friday night games, making it impossible to access event tickets and crucial information. "We want peace, everybody wants peace, nobody wants war". "I wanted to connect South Korea's past, present and future".
The meetings between North and South continue Saturday when President Moon holds a luncheon with the North Korean delegation.