The name of Hiroyuki Sonada's character, Musashi, is most likely inspired by the famed 17th century Japanese swordsman Miyamoto Musashi. The real Musashi is a cultural icon in Japan, and has been portrayed many times in television and film - most notably by Toshiro Mifune in the Samurai Trilogy.
Composer Ramin Djawadi was nominated for an Emmy Award for his music composition on his episode, eventually losing to another episode he himself composed in The Dragon and the Wolf (2017).
Thandiwe Newton delivered all of her Japanese lines on her own. The rest of the Japanese cast in the episode was impressed since she had to speak traditional, not modern, Japanese.
The long, spiked weapon wielded by Musashi is a sodegarami. In English it is sometimes referred to as a sleeve entangler. In reality it was designed not to kill an opponent, but to subdue them unharmed by tangling their clothing and immobilizing them.
"Akane no Mai" is Japanese for "Akane's Dance", Akane being the name (a proper noun) of Rinko Kikuchi's character. 'Akane' as a common noun is Japanese for 'madder', the herbaceous plant from the root of which a red-purple dye is obtained.