How did the death of the Empress Ci Xi affect China?
I think the best way to characterize the effect of the death of the Empress Dowager is to say that her death (along with that in the same year of the Guangxu Emperor) led pretty directly to the fall of the Qing Dynasty. The Empress had been holding the governmental system together, but there was really not another recognized legitimate leader waiting to take her place.
You could say, then, that her death led to the period of competition between various warlords that weakened China and helped allow it to be invaded by Japan. This competition eventually helped lead to the Communist takeover of China.
Defeat at the hands of the Europeans helped to set off a series of rebellions against the Qing. In the 1850s and 1860s, the Taiping rebellion, a semi-Christian movement under a prophetic leader, called for land redistribution, the liberation of women, and the destruction of the Confucian scholar-gentry. When the local gentry became sufficiently alarmed, provincial forces finally defeated the rebellion. Honest officials at the provincial level began to carry out much needed reforms, including railway construction and military modernization. Resources moved from the central court to the provinces, until the provincial leaders posed a real threat to the Qing government. The Manchus continued to obstruct almost all programs of reform, despite repeated defeats at the hands of the Europeans and the Japanese. The last decades of the dynasty were dominated by Cixi, the dowager empress. Cixi refused all attempts at reform. The dowager empress clandestinely supported the Boxer Rebellion from 1898 to 1901 as a means of ousting foreign influence. Her death eventually led to the collapse of the Qing Dynasty and evnetual invasion of Japan and later the beginnings of peasant revolts which later turned into the Communist party.