In Romance languages, the continent is known as the supercontinent "America", but in Germanic languages (like English) and other languages that borrow from it call them the "Americas" as two continents "North" and "South" America. So, for people to bring it over as 'America' can sometimes be seen as pedantry instead of insightfulness.
Well, yes, in theory you could use 'Amerikas' in German, but nowadays that's mostly because of a bad translation. It actually is correct German to speak of 'both America' - 'beide Amerika' (in singular).
South Africa? I would call it South Africa if that's what they want to be called. I definitely wouldn't call citizens of South Africa "RS Africans" or something unless they preferred that for some reason.