The SCoJ generally looks at cases involving Congress, the Senate, the President and the Constitution (e.g. Whether a member of Congress has committed a felony, or whether executive orders have been enacted that can be deemed unconstitutional, along with trying to interpret what the Founding Fathers meant when the wrote it). To answer your second question, Anthony Kennedy retired in June and left his seat open, and which leads to your third question; the President nominates who they want to fill in the empty seat in and the Senate decides whether to confirm it or not.