The Supreme Court usually only hears what kind of cases?
There is no telling which case or what kind of a case the Supreme Court will hear. If a case is simple, it never will get to the Supreme Court. Cases that reach the Supreme Court have gone through one or more appeals processes. Sometimes a appeal reaches the Supreme Court when a federal court of appeals has made a ruling different from another federal court of appeals. In that case, the supreme court is asked to certify an issue. That is a fancy term meaning to play referee. The Supreme Court certifies an issue when it takes up an issue where district courts of appeal have made different rulings concerning the application of the same law. (Sometimes the Supreme Court refuses to take up the issue. In that case it simply states, “Cert. Denied.”) Normally, all cases that reach the Supreme Court have come from the Federal Courts of Appeal or the Highest State Court. However, the Supreme Court reserves the right to sit as a court of original jurisdiction. The last time the Supreme Court granted a writ of Habeas Corpus was 1924. It retains that right. I doubt if any member on the Supreme Court has any idea under what conditions that would happen. Still, it retains that right.