What departments did Washington create and whom did he appoint to head them?
Department of Foreign Affairs: Secretary of State Thomas Jefferson
Treasury Department: Secretary of the Treasury Alexander Hamilton
War Department: Secretary of War Henry Knox
Justice Department: Attorney General Edmund Randolph
The departments he created are: Department of State,to deal with foreign affairs; the Department of War, to handle military matters: and the Department of Treasury, to manage finances. The heads were: Thomas Jefferson as secretary of state, Alexander Hamilton as secretary of treasury, and Henry Knox as secretary of war.
The president can apoint hisher choice to head each of the executive departments as long as congress each appointment?
That is correct. According to the Constitution, Article II Sec. 2, the President has the power to appoint whoever he wants, but with the "advice and consent" of the Senate (not the whole Congress, only the Senate). So yes, as long as the Congress agrees, the President can appoint whoever he wants. http://en.wikipedia.org/wiki/Advice_and_consent