judicial
The government does not belong to a branch, it has branches. The government is divided into three branches: the legislative, executive, and judicial. They all have different functions in terms of the law.
State supreme courts (or their equivalent) are part of each State's Judicial branch.
Yes, it makes sure that no one branch has too much power. A king or dictator is not wanted.
legislative
President Obama is in the Executive Branch of the government. (Congress is the Legislative Branch, and the Supreme Court is called the Judicial Branch.)
The three branches are Executive, Legislative, and Judicial. The president belongs to the Executive branch.
City Council.
Those three functions of government belong respectively to the legislative, executive, and judicial branches. In the US these are the Congress, the President, and the courts (particularly the Supreme Court).
judicial
The US President is head of the Executive branch of the federal government. The President's cabinet (advisors, department heads and all their employees) also belong to this branch.
The Senate and the House of Representatives are both part of the Legislative branch. The Legislative branch (Congress) creates and passes laws; the Judicial branch, headed by the US Supreme Court, evaluates challenged laws to ensure they are constitutional; the Executive branch enforces laws.
I assume you're asking about the branch of government, Executive, Legislative, or Judicial. The Judicial is the supreme court, with nine justices (the words judicial and justice come from the same root, see).