Congress has the power to declare war on any countries.
In general terms a professional who does this is called a "diplomat".
China fell under the complete control of foreign countries. Novanet - foreign countries were given total control over trade in China
Foreign countries were given total control over trade in China. <---novaNET!!
The unequal treaties of the 1850's and 1860's actually benefited China because the treaties called for trade to be established with China and other Asian countries. The trade with Asia accelerated, but then started to dwindle just before World War I.
Treaties, agreements, parterships, alliances.
These are called treaties.
executive agreements
The rules made for making relations with foreign countries is called foreign policy
They are called 'International Borders'
parts of countries surrounded by foreign territory is enclave or enclaves.
Countries do not have affairs in the way you imply in your question. Countries have foreign relations with other countries and the department that deals with these relationships is called the foreign affairs department.A foreign affairs department will have relations with all countries. some of which will be ambassadorial relationships.
The unequal treaties were considered unfair to China because they were forced upon the country by Western powers, exploiting China's weakened state to extract concessions that favored the foreign powers. These treaties often granted extraterritorial rights to foreigners, imposed unequal tariffs, and allowed foreign control of Chinese territory, undermining China's sovereignty and national pride.