Short answers, pulled from the story.
Hindi, formally Modern Standard Hindi, is an Indo-Aryan language written in the Devanagari script. It is an official language of the government of India and the lingua franca of most of the northern half of the country.
Hindi is the fourth-most-spoken first language in the world, after Mandarin, Spanish, and English. Counted together with the mutually intelligible Urdu, it ranks third, behind only Mandarin and English.
Hindi is not the national language of India. In 2010 the Gujarat High Court clarified that the constitution does not name any national language, though Hindi in the Devanagari script is an official language of the Union alongside English.
On the 14th of September 1949, the Constituent Assembly of India adopted Hindi written in the Devanagari script as the official language of the Republic, replacing Hindustani in the Perso-Arabic script. The day is now celebrated as Hindi Day.
Hindi and Urdu are two registers of the same language and are mutually intelligible, sharing an identical grammar and a core of Sanskrit-derived vocabulary. Hindi uses the Devanagari script and more tatsama Sanskrit words, while Urdu uses the Perso-Arabic script and more Arabic and Persian loanwords.
The term Hindi was borrowed from Classical Persian and originally referred to inhabitants of the Indo-Gangetic Plain. It traces back through Old Persian to the Sanskrit Sindhu, the name of the Indus River, which also gave the Greeks the words Indus and India.
Paramananda Jha took his oath as vice-president of Nepal in Hindi in July 2008, sparking five days of protests, burned effigies, and a general strike across 22 districts. The Nepal Supreme Court ruled the Hindi oath invalid in 2009 and left him inactive as vice-president.