My suggestion is nuntii fallaces.
I might be biased as a Finn, but I'm used to nuntii as the typical translation of "news".
It has a nuance of a delivered message, whereas auditio(nes) sounds more like a rumor.
It is up to you to choose which one is more suitable in any given situation.
I would say that using the word auditio already has a mocking tone when referring to news, but perhaps others will disagree.
If the news are wrong, then I'd call them falsi.
If they speak deceitfully, I might indeed call them fallaciloqui, but it strikes me a little odd to use such an adjective for news.
It depends on what you refer to with the word "news".
If you mean a "news broadcast on TV", then speaking deceitfully is a good pick.
But if you mean news in some other media or news as a "collection of news items" (instead of the broadcast that delivers them), I would use the adjective fallax instead.
The adjective you suggest is combined from fallax and loqui.
The word fallax on its own means "deceitful" or "fallacious".
Fallax means someone who tends to fallere; this is what the -ax suffix does.
In conclusion, the nouns nuntii and auditio(nes) are both possible, and so are the adjectives falsus, fallaciloquus and fallax.
It depends on what you want to convey exactly.
But I think nuntii fallaces is the most appropriate choice for "fake news" the way I understand the English term.