Example 1) is simply wrong, in British English at least and I think AmE too.
Example 2) is correct, but it's neither "a singular noun", nor "plural", nor "idiomatic".
"news" is an uncountable/mass noun, like butter, water, salt etc. So, it's never used with "a" (except if modified with a singular noun, eg "a news story / source / provider" etc; like "a butter dish", "a water jug" etc). I remember many foreign students of English making that mistake in my teaching days, largely because of it being a countable noun in their languages.
Like other uncountable/mass nouns, we can use "some/any/no + news", and also "a piece/bit etc of news".
"The news" can refer to news programmes / reports generally, eg
"Have you seen the news today?" (ie any tv / press etc presentation of current events)
And "the news" can also refer to a particular key news story that is reported in the media, or any personally important new occurrence:
"Have you heard the news? The prime minister lied about Grenfell! / Suzie's going to have a baby!"