This is admittedly an educated guess and may be applicable only in the US: But I believe the answer would be Municipal Courts or County-level court systems probably hear the most cases due simply to the sheer number of misdemeanor and traffic cases that are heard each day.
federal court
The Supreme Court is brought a large number of cases every year to review, but they do not have to hear all of them. They choose from cases that have already gone through state or federal courts where one of the parties was unhappy with the previous decision.
The Supreme Court of the United States was created in 1789. Most of the cases the court hears come from lower courts. Each year, the Supreme Court receives 7,000 or more requests to hear cases from lower courts.
evaluate the decisions of lower federal court
US Court of Federal Claims would hear those cases.
Cases involving federal laws, the U.S. Constitution, or disputes between states are tried in federal court. Federal court cases differ from state court cases in that they involve federal laws and are heard by judges appointed by the President, while state court cases involve state laws and are heard by judges appointed by state governments.
US District Courts have original (trial) jurisdiction over the majority of cases heard in the federal court system.US Special Courts, such as US Tax Court, US Bankruptcy Court, and the US Court of Federal Claims, also hear a large number of cases.
the Federal Court.
Generally, federal criminal cases are tried in US District Court.
Most federal criminal cases are tried in US District Court.
In most cases I have read the civil cases heard at the Federal level are cases that directly question someone's rights and apply to a large number of people. The cases heard at a local level can also be promoted to Federal cases. For example if you have a property dispute with your neighbor it will not go to federal court; however, if you have a court that disputes whether its legal for you to carry a concealed weapon or practice free speech you could proceed to the Federal Court.
Yes, it is a federal court.
Federal trial courts almost always have original jurisdiction in the federal system.
Bankruptcy Court is filed in Federal District Court, however, exemptions claimed are state regulated.
Federal tax cases
how the powers of the Supreme Court and federal law were extended by landmark court cases
US district courts have trial jurisdiction (aka original jurisdiction) over federal court cases.