Short answers, pulled from the story.
Henry Bessemer filed his first patent application in October 1855 and secured legal rights to the method a year later. The English inventor claimed inspiration from a conversation with Napoleon III during the Crimean War regarding better artillery materials.
William Kelly stated in a letter to Scientific American that he believed his discovery was known in England three or four years prior. Several English puddlers visited his facility and may have spoken of his invention upon returning home.
Robert Forester Mushet solved the issue by adding spiegeleisen to reintroduce carbon and manganese after burning off other elements. This alloy improved malleability and allowed the steel to withstand rolling at high temperatures.
The first commercial production began in Sheffield in 1858 using imported charcoal pig iron from Sweden. The core mechanism involved blowing air through molten pig iron inside a large vessel called a converter.
Manager Edward Martin provided test equipment and helped draft a patent issued in May 1878. The invention used dolomite or limestone linings instead of clay within the converter vessel.