Please give a brief comparison and contrast the responsibilities of the national, state, and local governments.
Let's deal with what is exclusive to each one. The problem is that lots of responsibilities are shared and jurisdictions mixed.
They may print money, though that has been farmed out to the Federal Reserve, which is a private consortium of bankers.
They regulate any commerce (or anything) that crosses state lines. They deal with disputes among or between states (such as the water fight among Nebraska, Colorado and Wyoming). Of course, all international trade is federal in nature. No state, in other words, can make its own foreign policy.
Congress (the one house of the legislature only) can declare war. This has largely fallen into disuse as presidents have unilaterally taken the US to war.
All military forces are federal. This includes national guards that are under federal jurisdiction. All national guard units are under federal martial law.
The Senate (the other house of the legislature) can make treaties with foreign powers. They do not ratify them, but the Senate alone can approve one already ratified. Article II of the Constitution states that the President "shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two-thirds of the Senators present concur." So a super-majority of senators have to agree to a treaty ratified by the President.
The following posting provides an outline of government responsibilities.