Thames Iron Works Football Club, founded in 1895, went on to become West Ham United FC.
The "lullaby" that Rose sings is an American folk song called "In the Pines" that dates back to the 1870s. It's also known as "Where Did You Sleep Last Night?" and "Black Girl". It was made famous by musicians like Leadbelly and Bill Monroe in the 1940s, and has been covered by artists from many genres including Nirvana and Kid Cudi.
Gower was talking about seeing the effect of the Maxim machine gun, the first, fully automated machine gun, as it cut down and shredded the Africans at Bulawayo. He was not referring to the deaths of British soldiers.
The episode title "Men of Iron, Men of Smoke," is spoken by Felix Hackman (Owen Teale). "I loved that boy. Men of iron? Men of smoke is all we are."
In Rachel's office there's a board next to the window with some leaflets and other scraps of paper on it. They seem to be pinned with wat looks like thumbtacks, although these have yet to be invented. In 1903 to be precise.