Explanations

Colors/色

色 means color in Chinese and Japanese. It also refers to metaphorical colors such as mood, appearance, tone, lively elegance, and romance or sexual pleasures. Musashi uses 'colors' as a euphemism for sex. Erik finds it archaic but never mistook his meaning.

Flute Playing/Shakuhachi

A shakuhachi is a Japanese flute. An end-blown flute, the word is borrowed in Japanese slang to mean fellatio. 'Flute playing' is used in Kintsugi rather than American slang because, while the entendre should be just as clear as to Japanese, it should seem less vulgar to an English-speaker.

Family Registry/Koseki

In many East Asian countries, a single document serves the purpose of a marriage certificate, birth certificate and death certificate. This document is the family registry, koseki (戶籍) in Japanese. This type of record keeping requires a registered family to share a surname.

Spoiler: Kintsugi

At the end of Kintsugi, Erik and Musashi talk about making a family together, i.e. getting married. Saharinese marriage law, which is inspired by Japanese marriage law, does not require a ceremony only that the husband and wife create a family registry. At that time, same-sex couples could not make a family registry. The idea that a family must have the same surname is ingrained in their understanding. This is why it matters whether Musashi joins the Hayate family or Erik joins the Toda family.

Goldfishy

Spoiler: Golden Lotus

In Golden Lotus, there is a chapter entitled "Goldfish." This comes from a comment Ren's roommate makes, "You walked in here, don't pretend you're goldfishy." The roommate misspeaks. Kinchou-sei (緊張性, literally 'tension-nature') is the Japanese word for 'catatonic.' Kingyo (金魚) is 'goldfish'. The roommate says 'kingyo-sei', which is nonsense best rendered as 'goldfishy.'