They look like the captain from Tintin.

I'm interested in knowing how the Japanese knew about all of this

World is smaller in the past than we generally think because we're given a thin slice of history in school

Trade and travel. A lot of Japanese politics at this time was heavily influenced by America. Particularly the idea that "all men are created equal".

I like how the uniforms look authentic (to my untrained eye), but all the vegetation is distinctly Japanese.

bro those boots are fabulous

I choose to believe that the cloud thing in the background started out as My Fuji and the artist realized their mistake.

Japan had been forcibly opened to trade by the US Navy a decade before the US Civil War, so in 1879 they were getting news like any other 19th century country - photographs, newspapers, and telegraphs. The Civil War had been over for 14 years at that point, but was still a major topic in US culture, so any Japanese fellow who wanted to find out about the details would find it fairly easy to do so.

Your fuji must've been a sight-to-see if a Edo-era artist was thinking about it in the late 1800's