Answer:
This is a form of government run by elected leaders. - Republic. Remember that the word "Republic" comes from Latin <em>res publica,</em> Which means "public affair". This is to say that government is a public affair and therefore, must be elected by the people.
This is a type of government in which a group of individual states are united under a strong, central government. - Federation. Just like the United States or Germany, states share some things such as military, but are independent in other matters.
This is a system of government in which the people participate directly in making all public policy. - Direct Democracy. This is how it works in Switzerland. The government runs referendums every year, and citizens vote to approve or disapprove policies.
This is form of government in which a monarch is the head of state but his or her powers are restricted by law, usually within a parliamentary system. - Constitutional Monarchy. This is how it works in the UK or in Spain. The Monarch (Queen or King) is the head of state, but his or her powers are ceremonial. The real power is held by the prime minister.
In this type of government, the elected head of the executive branch acts independently of the legislative and judicial branches. - Presidential Democracy. Just like in the United States, the president is a republican, but one of the chambers of congress (the house of representatives) is being controlled at the moment by the democrats.
In this type of government, there is no clear-cut separation of powers between the legislative and executive branches, though the legislative has most of the governmental power. - Parliamentary Democracy. For example, the UK, where Borish Johnson is prime minister because he holds a majority in parliament.
In this type of government, the institutions of the state are governed as a single unit, with one constitutionally created legislature. - Unitary State. This is the opposite to a federation. For example France.
This is a type of government in which power is held by a single, self-appointed ruler. - Autocratic. For example, Robert Mugabe's Zimbabwe or Fidel Castro's Cuba.