With respect to Taiwan: what is it that constitutes a nation, if not the common belief of its people that they are a nation, combined with the reality that they are under the control of a government which they recognise as their own?
So is the common believe of a group of people enough? Or does it need the recognition of others?
Partly, it depends on whether the debate over nation status is a merely one of linguistics and categorisation or whether we're making ethical arguments.
When Japan annexed Korea, did the Korean people cease to constitute a nation? When Japan annexed Taiwan, did Taiwan cease to rightfully belong to the Chinese government of the time?
(As an aside, I think that no-one talking about the Taiwanese company's involvement in IP theft is a pretty good example of how the press is incentivised to lead with a sensationalised narrative that inflames sentiments, how people focus on facts that fit a pre-existing narrative, and a general bias against China).