I never really thought about those words.
For sure I say “The news is”.
With headquarters I thought about it too much and can’t think of how I do it spontaneously. I think I say “The headquarters are”. But it might depend on whether it’s first second of third person.
I would only believe the latest editions of dictionaries. Words change through time, and what once was may not be true nowadays. And when it comes to dictionaries, I always use Oxford as my main source of information.
News only has singular form of verbs, is/was, etc. However, Oxford dictionary states it is primarily a plural noun, so I wouldn’t say it’s like news.