Powers of the judicial branch: declaring laws constitutional or over presidential impeachment hearingswhich power should be added to this list?

Another power to add to the list would be:  Deciding the legality of executive orders.

An example would be Executive Order 13769, which was titled, "Protecting the Nation from Foreign Terrorist Entry into the United States."  President Donald Trump signed this order on January 27, 2017, in the first weeks of his presidency.  Commonly called the "travel ban," this order suspended travel to the United States from a number of countries with a majority Muslim population.  The order immediately was challenged in the courts as unconstitutional.  The Trump administration was compelled to replace Executive Order 13769 with a  revised version that it hoped would stand up to court challenges, Executive Order 13780, signed in March, 2017.

Protecting and assisting  u.s. citizens  living or traveling abroad; assisting u.s.  businesses  in the international marketplace; coordinating and providing support for international activities of other u.s. agencies (local, state, or federal government), official visits overseas and at home, and other diplomatic efforts.keeping the public informed about u.s. foreign policy and relations with other countries and providing feedback from the public to administration officials.providing  automobile registration  for non-diplomatic staff vehicles and the vehicles of diplomats of foreign countries having  diplomatic immunity  in the united states