This is the countable noun, so it takes a and s: a Nepali, two Nepalis. It always keeps its capital letter, like the names of other peoples. The source's wording covers both someone born in Nepal and someone of Nepali descent, so a person born elsewhere to a Nepali family can be described this way too. English also has the older word Nepalese, which works as both noun and adjective; Nepali is the form the source leads with and the one used for the language.

As a language name this is uncountable, so it takes no a and no s: she speaks Nepali, a book in Nepali. It behaves like every other language name in English — capital letter, and the preposition in for something written or spoken in it. The same spelling is also the word for a person from Nepal, and what tells the two apart is the grammar around it: an a or an s in front of or behind the word points to the person, a bare Nepali after speak, learn or in points to the language.