@Hendrik_2000 Please provide me evidence , from Song written records, that the Song considered the Liao Chinese?
They perfectly fit in definition of all under heaven when they submit to Tang dynasty and accept the suzerainty of Tang imperial power. Tang power rule indirectly thru this conquered people as long as they submit themselves to Tang power and adopt Chinese civilization. They were then given Chinese surname, title and Chinese princess or imperial maid as wife to the chief. This people are considered half Chinese so yes they are not 100% Chinese. But so what, some of the Chinese kingdom in the south like Chu(present day Hubei province) or Wu(present day Zhejiang) or Yue(present day Fujian) are considered half Chinese But they are the key component of Han or Chinese nation nevertheless.
There were eight tribes, namely the Xiwandan 悉萬丹, Hedahe 何大何, Fufuyu 伏弗郁, Yuling 羽陵, Rilian 日連, Piqie 匹挈, Li 黎 and Tuliuhan 吐六干 (or Tuliuyu 吐六于), all in Chinese transcription. The Khitan federation first presented tributes to the
北燕 (409-436), which on her part invested the qagan ("khan") as Prince Guishan 歸善王.
During the
北魏 (386-534) the Khitans regularly presented tributed to the Wei court in the shape of horses and animal skins. There was a regular border trade in Helong 和龍 (modern Chaoyang 朝陽) and Miyun 密雲. In 553 the Khitans were heavily defeated by the armies of the
北齊 (550-577) and lost a large part of their population, and also many cattle. In 584 they declared their submission to the
隋 (581-618). During the early years of the 7th century the family Dahe 大賀 wielded great power among the chieftains and unified the Khitan tribes in a federation that was able to raise 34,000 males as troops. During war all eight tribes joined together, yet for civilian activities like hunting, the tribes acted on their own. In 619
The 唐 (618-907) court set up the prefecture of Liaozhou 遼州 which was to be indirectly administered by the Tang through the Khitan chieftains as quasi-state officials of the Tang. In 648 the (dudufu 都督府) of Songmo 松漠 was established, with 10 prefectures. Kuge Qagan 窟哥, highest leader of the Khitan federation, was appointed commander-in-chief (dudu 都督) and was allowed to bare the imperial surname Li 李. he was furthermore given the title of District Baron of Wuji 無極縣男. His descendant Li Jinzhong 李盡忠 joined with a powerful chieftain, Sun Wangrong 孫歲榮, in rebellion against the Tang in 696. After his first victory at Yingzhou 營州 he adopted the title of Supreme Qagan 無上可汗. His sudden death and the takover by Sun Wanrong ended this short period of dominance.
The Tang sought for support by the and defeated the Khitans. The Khitans thereupon submitted to the Later Türkic empire for a decade or so, but in 716 again, the highest leader Li Shihuo 李失活 declared his submission to the Tang. He was appointed commander-in-chief of Songmu and given the title of Commandery Prince of Songmo 松漠郡王 and granted the title of great general of the insignia of the imperial encampment (xingzai jinwu da jiangjun 行在金吾大将军. He was also given a Chinese princess to his wife.
His successor Li Guozhe 李過折 was killed in 735 by a certain Nili 泥禮, and this was the end of the domination of the family Dahe. For defense measures the Chinese court set up the military commands of Fanyang 范陽 and Pinglu 平盧. Yet instead of protecting Tang China against the Khitans, the military commissioner An Lushan 安禄山 used these garrisons as a base for his rebellion against the Tang dynasty.
After the rebellion was ended, the Khitans again submitted to the Tang and presented tributes for a while, before the Khitans came under the sway of the
回鹘 that dominated the western part of the the steppe in the late 8th century. In the mid-9th century the Uighurs were defeated, and the Khitans again became subject to the Tang dynasty. The federation was during that time led by the family Nian 輦 until 907 when the qaganship was taken over by Abaoji 阿保機 from the Yelü family 耶律. In 916 he united all Khitan tribes, proclaimed himself not only qagan, but also emperor (as Liao Taizu 遼太祖, r. 907-927), of the empire of the Qidan (Qidan guo 契丹國).
Abaoji had created an own script for the Khitan language, modeled on the Chinese script. He also had imitated the administrative structure of the Chinese empires, established a capital and adopted a reign title. After the destruction of the empire of 渤海 in the east, he also adopted the dynastic name of Liao, according to the river in the heart of his empire. The Liao empire dominated the weak dynasties in China's north during the first half of the 10th century and was a match for the 宋 (960-1279), founded in 960. 
