Since the Constitution invests the Congress (elected by the consent of the governed) with the power to regulate trade with foreign nations, the Constitution leaves it to Congress to define the particular crimes. Treason is the only defined crime in the Constitution, but that doesn't prevent Congress or the state from passing laws which define other crimes and set consequences for committing such crimes.
Wrong. There are three crimes defined in the constitution and in every case, the Congress is given power to make laws which deal with those crimes. They are given no power in the constitution to even DEFINE crimes not listed already.
You don't have the power to tell your neighbor who he can trade with. And you can't give that power to the government if you do not posess it already.
Congress has the power to regulate commerce between the states and foreign nations. They do not have the power to eliminate trade. The word regulation should provide a clue but the fact that you cannot force anyone to stop trading is the nail in the coffin for this particular argument.