The United States’ various embassies in foreign nations throughout the world are administered by which entity of the United States

The President appoints the ambassador.

Explanation:

The US embassy exists in almost every country in the world except for a small number of states where the US has no embassy, and some of these countries are North Korea and Iran. The ambassadors are appointed by the President of the United States of America, and Congress must confirm their eligibility. The function of United States ambassadors is to represent America through diplomacy in foreign countries. The Ambassadors generally present their reports to the Secretary of State and his assistants, who further report to the President and Congress on the situation in a particular country and the quality of bilateral relations between that country and the United States.

they had freedom from the government and from the affairs

this doesn't support enough information to answer the question.