I think False/Fake News exists.
I think it's existed long before the last 5 years or so.
I think it's term has sort of been abused lately, though.
It seems to mean "news I don't want to hear about" more than purposefully-inaccurate news, though.
Misleading news is nothing new. As you indicated, it existed far before the modern era. (Ever read Pravda?) I think the reason it gets more traction now is social media. Because individuals have the ability to tailor their news sources to whatever fits their preconceived narrative, it is easier to pigeon hole individuals into
only believing certain sources of news and discounting others as 'fake news'. Trump's favorite catch phrase.
From my perspective, what bothers me is not necessarily outright 'fake' news, but the obvious bias various news outfits have when it comes to the types of stories they publish. It's no revelation that the Drudge Report leans heavily right and its equally obvious that the Huffington Post leans heavily left. The bias has also found its way into the 24 hr news channels which in my opinion are all garbage now. Fox News pushes the Republican agenda. MSBNC pushes the Democrat agenda. And CNN is essentially left leaning with a heavy emphasis on what I call 'disaster porn'. Hence their 'Breaking News!' ever five minutes methodology.
What I try to do is focus on news sources that, while not perfect, at least give me the ability to review the information more dispassionately. BBC News from my perspective is pretty decent. It does lean left, but it has a world view including reporters in different geographic regions like Singapore. This gives different perspectives which I like. Bloomberg does that as well with offices in Hong Kong and Australia. And also, the PBS Newshour is still, in my opinion, a pretty well rounded news source.
Nothing of course is perfect.