As for Hong Kong, the blessed Lady gives us the answer there as well. As she points out, the Falklands was no precedent for the British approach to Hong Kong – the legalities of the case were mostly on China’s side. Britain did claim sovereignty over the island of Hong Kong itself under the Treaty of Nanking in 1842, which China refused to recognize, but there was no doubt that the lease to Britain of the New Territories was up in 1997, and there was nothing Britain could do legally to stand in China’s way. And Hong Kong itself was and is utterly dependent on the New Territories for water and supplies.
So the discussions revolved around whether or not Hong Kong would remain essentially an Anglosphere outpost (in terms of law, economic system etc) or be absorbed back into China. Mrs T’s stance was for the former option. When Deng Xiaoping told her China could walk in an take Hong Kong that day (this was 1982), Mrs Thatcher replied that they could indeed do so and she could not stop them. “But this would bring about Hong Kong’s collapse. The world would then see what followed a change from British to Chinese rule.” From that point onwards, a startled Deng became more accomodating. The result is that capitlaist Hong Kong survived.