Some of the translations in the first video are way off( didn't see the others) but thats not surprising. You Chinese can't even understand Korean but readily make accusations about Koreans distorting history. The translations suck period. The person in the video isn't even taking sides, hes asking questions while taking a neutral stance. The same show deals with alien conspiracies, government black projects and other entertainment value documentaries. Its a television show, not a government sponsored history project that is taught to children.
That said, the video is 100% accurate although the translations and your assertions are typical Chinese fabrication and poor understanding of the Korean language. It is historical fact that the Jin dynasty has Korean roots. The founder of the Jin Dynasty, Emperor Taizu of Jin was descended from the Wanyan clan which was founded by Wanyan Hanpu who was recorded in Chinese and Jin records as having come from Goryeo(Korea). This isn't surprising in the least since the Koreans and Jurchens were neighbors and regularily mingled with each other.
Hanpu - Wikipedia, the free encyclopedia
Emperor Taizu of Jin - Wikipedia, the free encyclopedia
The Jin later became the Manchus and the Manchus conquered China. So really, exactly what fabricaiton is the video making?