The court can certainly administrate a proceeding to determine the guilt or innocence of the accused but is bound by existing law that dictates the authority the court has to do that.
The court can certainly mediate disputes by interpreting what the law says and the LAW, not the court, determines what the court's ruling will mean for the disputing parties.
No court was intended to have authority to tell the President what bills he could sign into law and what bills he could not. No court was intended to have authority to tell the legislature what laws it could pass. If a law is challenged, the court can certainly rule on whether law is in conflict with any other law including the Constitution, but it must be up to the legislative body to then rescind or change that law to conform. It is not up to the Court to do so.
That way we have separation of powers. A court given power to dictate to the legislative body or chief executive what it must and must not do is a court with unlimited power.