> Author Sarah Churchwell asserts that it was Woodrow Wilson who popularized the phrase 'fake news' in 1915, although the phrase had been used in the US in the previous century.
> The term actually dates from the late 19th century, when it was used by newspapers and magazines to boast about their own journalistic standards and attack those of their rivals. In 1895, for example, Electricity: A Popular Electrical Journal bragged that “we never copy fake news,” while in 1896 a writer at one San Jose, California, paper excoriated the publisher of another: “It is his habit to indulge in fake news. ... [H]e will make up news when he fails to find it.”
[1] https://en.wikipedia.org/wiki/Fake_news#20th_century
[2] https://www.csmonitor.com/The-Culture/In-a-Word/2019/0726/Su...
https://twitter.com/CraigSilverman/status/522179364767924224 and https://www.theverge.com/2014/10/22/7028983/fake-news-sites-... are good examples of its use pre-Trump. By the time Trump started applying it to actual news outlets, it was already in relatively common use.
https://www.cnn.com/2016/12/08/politics/hillary-clinton-fake...
December 2016 Hillary Clinton decides to use the term in reference to recent events like her losing the election. The media picks up on it and the term starts to lose its meaning. Then Donald Trump, always with a nose for catch phrase politics, picks up the term and runs with it, a turn of events that someone on HN called a huge "own goal" by the media, and I can't say I disagree with that assessment.
For more analysis of this cultural specimen:
In your examples the word "fake" is used as an adjective to the noun "news site". As in "a fake news site".
"fake news" as it used today is a noun in its own right. As in "that's fake news"
See also "alternative facts".