What supernatural beliefs did people hold in the early stages of Chinese civilization? How did they compare with those held by the people of Egypt? Support your views with specifics.
I think it largely depends on what your definition of supernatural is. What we in the west may consider magical, mythical or supernatural, in Chinese or Egyptian culture may be taken more seriously. Conversely other cultures may view Judeo-Christian religious beliefs, practices, customs and traditions as bizarre and might classify them as supernatural. However I think that the religious history of ancient China and Egypt are fairly distinct, although the both put emphasis on ancestry and polytheism.
Supernatural things both ancient China and Egypt had in common were the practice of magic and the desire for immortality and the worship of heaven and earth. Egyptians thought heaven and earth mirrored each other. Some Chinese still worship heaven and earth. Chinese Taoism grew out of the practice of magic and the quest for unending life. Egyptian worship of Osiris emphasized immortality.
I think the greatest commonality between China and Egypt is the idea that our souls live on after death in some form or another. This is why there are mummies in both cultures. Many early cultures had this same belief.
The early Chinese, during the Shang Dynasty, worshipped a supreme deity known as Shang-di who controlled human destiny and nature; but he was so far above mere mortals that he could only be approached by the intervention of ancestors. This was an important development in the belief in veneration of ancestors. They also believed that ghosts, spirits and monsters inhabited the birth. They had a creation belief in that a creation deity had sired ten sons and twelve moons, but all but one of each had been shot down by an archer which saved the earth from destruction by overwhelming heat and light. They practiced both human and animal sacrifice. Most humans who were sacrificed were buried alive. Sacrificial victims were often "barbarians" captured in battle.
In Egypt, a pantheon of Gods was worshiped, primarily the God Re who represented the sun. Egyptian Gods were typically depicted as having both human and animal features. Re had the head of an eagle or hawk, because its sharp eyes allowed it to see at great distances. Anubis, the god of Mummification, had the head of a Jackal.
Mummification was probably the most important aspect of Egyptian religion. It was based on their strong belief that the dead would live again. Originally, only the Pharaoh, who was himself worshiped as a God, was believed to resurrect from the dead; but later the belief developed that all would live again.
An important element of Egyptian religion was the veneration of the Nile. The Nile was not worshiped as a god, but was highly venerated. Its floods were responsible for the continuation of Egyptian society. The ancient Chinese did not venerate the Huang He river which also provided sustenance with its floods as did the Nile. The primary difference was that the Nile's floods were predictable; in fact it was believed that the Pharaoh had the power to control the flood. The Huang He's floods were very arbitrary and capricious, so it was something of a necessary evil.