Your story is very incorrect.

Taiwan was originally part of various European empires (Spanish, then Dutch) before being conquered by the Ming admiral Koxinga during his exodus to Taiwan after the fall of the Ming Dynasty in the 1600s. He was intending to use it as a bastion to fight back against the Qing and restore the Ming dynasty, but he ended up dying of disease. His son swore loyalty to the Qing and eventually the island was taken over by a Qing naval force.

In 1894-1895, the Japanese and the Qing fought in the First Sino-Japanese War. The Japanese victory got them to claim Port Arthur (now Dalian) and the island of Taiwan. They started developing the island in order to turn it into another part of Japan, encouraging Japanese assimilation and building many permanent Japanese institutions that left a lasting impact on Taiwanese culture.

After Japan's defeat, China declared that it was going to reclaim all the former Japanese lands that it had a claim to. This included Manchuria, the Japanese concession in Shanghai, and Taiwan. Chinese forces were landed on Taiwan in October 1945, and Taiwan was formerly surrendered back to China.

Around this time, the civil war between the Chinese Nationalists (the ruling government) and the Communists resumed. Due to a variety of reasons which will only complicate the answer, the Communists were victorious and the Nationalist government fled to Taiwan. The Communists were decisively defeated in an attempt to seize a vital island necessary for an invasion of Taiwan, and the onset of the Korean War caused the US to take an anti-Communist stance, essentially guaranteeing Taiwan's independence from the mainland regime.

As for Hong Kong, as part of a British victory over the Qing in the Opium wars, Britain was ceded Hong Kong in perpetuity and other nearby territories for 99 years. As a result of WW2, Britain agreed to return all of Hong Kong back to the mainland in 1997. Which they did. China also received Macau from Portugal in 1999, which had been colonized by the Portuguese since the 1500s.

The only other former Chinese territories that have not been returned are Tannu Tava (which was annexed into the Soviet Union, now Russia), Mongolia (which is now independent), and Outer Manchuria (currently Primorye, the Russian Far East, including Vladivostok).

The vital detail you're missing is this:

As well as fighting the Japanese, the Chinese government was also fighting a Communist rebellion under Mao Zedong. They (at least in theory) put aside their differences to co-operate - a bit - in fighting the Japanese but when the war was over they went right back to it, and in 1949 Mao's communists finally won. However, instead of surrendering, the nationalist government under Chiang Kai-Shek fled to the island of Taiwan. The communists weren't in an immediate position to launch an invasion and the US has been pretty keen to maintain Taiwan ever since.

So in fact, Taiwan has never declared itself an independent country - its official name is the Republic of China and it maintains (at least officially) that it is the rightful government of the entire country, that is temporarily under the control of some rebels. In fact, the RoC government held China's seat on the UN Security Council up until some time in the 60s or 70s, I believe - it was because the Russians had walked out over this that the US was able to get the resolution it needed to intervene in Korea.

TL:DR, Taiwan was returned to China, and represents all that's left of the former government after the Communists conquered the mainland.

Hong Kong (and Macau, which was Portuguese) go back further, to the period when Imperial China was strongarmed by various western powers into signing away trade and commercial rights at its ports, and then allowing said powers to effectively annex said ports. The UK leased Hong Kong on a long-term basis and when the lease came to an end in 1997, we gave it back. However, by that time, the people of Hong Kong were used to having freedom and democracy, and particularly economic freedoms, and didn't want to join a communist dictatorship, so a deal was struck with China whereby Hong Kong got to stay basically as it was - China accepted this because the massive amounts of money made there would help their economy.