Short answers, pulled from the story.
Ruthenia is a Medieval Latin exonym for Rus', the East Slavic lands and peoples who called themselves Rus'. Western European writers adopted the Latinized form to describe the territory in their own alphabet; the word Ruthenorum appears in European manuscripts from the 11th century onward.
The ethnonym Ruthenians referred to East Slavic and Eastern Orthodox peoples living in the Grand Duchy of Lithuania, the Kingdom of Poland, and later the Polish-Lithuanian Commonwealth and Austria-Hungary. In practice the term was applied mainly to Ukrainians and sometimes Belarusians in the territories of modern Belarus, Ukraine, eastern Poland, and parts of western Russia.
Carpathian Ruthenia is a highland region south of the Carpathian Mountains, including the cities of Mukachevo, Uzhhorod, and Prešov. It became part of the Kingdom of Hungary in the year 1000 and was incorporated into Czechoslovakia as Subcarpathian Rus' in May 1919 before being annexed to the Ukrainian SSR in 1945.
Avhustyn Voloshyn declared the independence of Carpatho-Ukraine on the 15th of March 1939. On the same day, troops of the Royal Hungarian Army occupied and annexed the region.
Ruthenium is a chemical element isolated in 1844 by Karl Ernst Claus, a Russian naturalist and chemist of Baltic German origin, from platinum ore found in the Ural Mountains. Claus named the element after Ruthenia to honor Russia.
Rusyns are a group of East Slavic highlanders concentrated in the Carpathian region whose ancestors kept the historical name Rusyn rather than adopting the Ukrainian national identity. Since Ukrainian independence in 1990-91, the Ukrainian government has maintained that Rusyns are part of the Ukrainian nation, but parts of the population in Zakarpattia Oblast continue to identify as Rusyn, sometimes alongside regional identities such as Boyko, Hutsul, or Lemko.