The answers would be as follows
a. The emperor threatens his neighbors to make them subdue to China
b. Mongolia
c. The Emperor wants to assert his suzerainty.
Explanation:
a. The emperor threatens his neighbors to make them subdue to China
The time of the medieval era was a difficult one for Chinese borders being constantly claimed by assailants so he wanted to assert his might on thee world.
b. Mongolia
The mongols were constantly invading China from North and the West and he is acknowledging that.
c. The Emperor wants to assert his suzerainty.
The emperor wanted the people to know that he was strong and would be able to deal proactively with border threats and look to expand the empire if provoked.