How did control of trade made it possible for
imperial nations to gain power in
China

The primary motive of British imperialism in China in the nineteenth century was economic. ... Clashes between the Qing government and British merchants ultimately escalated into the infamous Opium Wars. As a result, the British were given the island of Hong Kong and trading rights in the ports of Canton and Shanghai.

  the domino theory states that  if one country in a region came under the influence of communism, then the surrounding countries would follow in a  domino  effect.