China has been a country for longer than the history of European civilization. They do not subscribe to the view that nothing that happened before 1945 matters the way Americans seem to.
China also makes the claim of 1000s of years of history but Taiwans inclusion in that history is about 200 years. And of that less than 10 was a province that China still didn’t govern or control. It was more or less just something they said to deter Japan. So historically China has never ruled over Taiwan. Japan has more claim to Taiwan than China as it actually ruled and controlled Taiwan.
Not if you're a nationalist, since most of Taiwan is ethnically Han, not Japanese.
No, China has not been a country for longer than European civilization. That CCP propaganda claim is the equivalent of saying that the European Union has been around for 8000 years because Plovdiv, Bulgaria was founded in the 6th Millennium BC.