Short answers, pulled from the story.
Osamu Tezuka founded Mushi Production as a direct rival to Toei Animation, his former employer, after his contract with Toei expired in 1961. Tezuka wanted to compete against Toei and establish his own studio for television and film animation.
Mushi means insect in Japanese. Tezuka chose the name because he had a deep affection for insects and was a fan of entomology from a young age. His pen name Tezuka is also derived from the Japanese word for firefly.
Mushi Production created Astro Boy (Tetsuwan Atomu), which ran from 1963 to 1966, along with Kimba the White Lion, Princess Knight, Goku no Daiboken, Dororo, and Ashita no Joe, among others. The studio is credited with pioneering television animation in Japan.
Yes. Frosty the Snowman, which aired on the 7th of December, 1969, was an American production by Rankin/Bass Productions with animation provided by Mushi Production. Paul Coker Jr. handled the production artwork and Yusaku "Steve" Nakagawa supervised the animation.
Cleopatra, released by Mushi Production on the 15th of September, 1970, was the first Japanese X-rated animated film. It was part of the studio's Animerama adult-oriented feature film series and was also noted in the United States as next-to-first to receive the self-applied X rating.
Mushi Production declared bankruptcy in 1973 after years of financial difficulties. Scholar Morisawa argues that Tezuka proposed unrealistically suppressed production budgets to underbid competitors, contributing to low profitability at Mushi and across the anime industry at the time.