Does the FBI have the authority, without the appointment of a special prosecutor, to investigate the President? They report to him. This would seem like a massive conflict of interest at the very minimum.
Did the FBI investigate Nixon?
IMO, the FBI has no authority to investigate an elected president. Whatever the president does in the foreign field is completely covered by his Article II powers. They are NOT the arbitrator of what is or what is not within that scope. They are not the fourth branch of government.