I would have thought most educated Australians understand the difference between "red states" and "blue states", and would identify California as a "blue state" and Alabama and Tennessee as "red states". (The "red state"/"blue state" terminology only dates to the 2000 election, but the reality it refers to is older than the label.) California is on average politically much more left-leaning than Alabama/Tennessee, and on average significantly less religious. And the difference between a West Coast accent and a Southern accent. Obviously that kind of mental model of the US is simplifying a lot of things, but it does accurately identify some real differences in US culture.
I am university-educated, and so are most of my family and friends, so I'd imagine less educated people may on average have a simpler mental model of the US. If you watch Australian TV news, there is frequest coverage of US national politics (regular but shallow on the commercial networks, serious and in-depth on public broadcasting), so I don't think it is uncommon for Australians to acquire this sort of basic understanding of the US. Even people who don't watch the TV news or read the newspaper are likely to watch a lot of US TV shows and movies, and so tend to acquire a basic (if simplistic and distorted) understanding of US culture through that.
Maybe there is less coverage of the US in the Scandinavian media? Australia is probably more influenced by the US than the global average, although I thought US media exports were popular in most countries on earth, and US politics arguably gets more international coverage than the politics of any other country.
> They will have heard of Tibet, but won't know the dynamics between Tibet and mainland, or even Hong Kong and mainland.
I would have thought most educated people would know at least a little bit about the dynamics between Tibet and the Chinese government. Again, I don't know what is in the news in Scandinavia, but there have for years been frequent stories in Australian media about the conflict between the Dalai Lama and Beijing–every time the Dalai Lama visits Australia (he's been here several times), Beijing complains about his visit, and the possibility that he might meet Australian politicans, and the controversy is reported in the media. Sympathy for the cause of Tibetan independence is common (although certainly not universal) in Australia, and I thought that was true of the US as well. Even people whose media consumption is much more low-brow than mine would probably remember Richard Gere's outspoken support for it.
The conflict between Beijing and the Uighurs in Xinjiang gets global media coverage too, so I'd expect a lot of people have at least heard of it, although it hasn't impacted the popular consciousness to anywhere near the same degree as the Tibet issue has. In 2009, Uighur activist Rebiya Kadeer visited Australia, and the Chinese government got very upset over the whole thing, and that led to extensive coverage in the Australian media. (She's come back again since, but subsequent visits didn't receive the same attention; most people probably couldn't remember her name, I myself had forgotten it, but I remembered the furore.)
I can remember Australian media coverage of the Hong Kong democracy movement from pre-handover times to today. The umbrella protest movement of 2014 received extensive media coverage in Australia.
Possibly China gets less news coverage in the US or Scandinavia than Australia, so it may well be true that the average American or Scandinavian knows less about China than the average Australian does.