I already knew "Русский" before trying Russian here, but only now I'm aware of the ий and ая endings being related to adjectives. Cool reaching this part; everything seems to connect now!
Also, the Russian Spelling Rules changing русскый -> русский because of the к at the end of the stem русск-. The "dictionary" masculine singular nominative/accusative (inanimate) adjective ending is -ый
"The Russian tongue" = "The Russian language"
"A Russian tongue" = either "A Russian dialect" or "[The organ inside a Russian mouth]"
Ambiguously yes. [ русский ] is some Russian masculine noun adjective, может быть; алфавит, балет, борщ, вальс, глагол, гриб, диалог, театр, текст, фестиваль, флаг, экзамен, i.t.d., и так далее.
Chinese, Indian, Indonesian, Brazilian, ..,what ? agriculture, business, culture, demography, dentistry, diplomacy, economy, people, person, population, zoology, and so on.
In a sentence, you could: Вы знаете русский язык = "You know Russian/the Russian language". Depends on how literal or formal you want to be. It should be obvious from the exercises that язык isn't necessary, either.
Although the point of the exercise seems to be to include both words, https://www.duolingo.com/lwGu6 lwGu6 (see below) reported 6 months ago that "Russian" alone was accepted.
Sitesurf has said elsewhere that it depends on the formality the speaker chooses to use. "The Russian langauge" is very formal in English, and русский язык is formal in Russian, the kind of wording seen on a text-book or a syllabus. язык is often dropped, as "language" is dropped in English.