Theft may be an act in violation of either state or federal statutes, depending on the crime committed (identity theft is a federal offense; petty theft is typically a state offense).
Added: The location of the occurrence is also important. Felony offenses occurring on federal property, (national parks/forests, military installations, etc) are prosecuted as crimes occurring on a 'federal reservation' but can be waived to the local jurisdiction for prosecution by the US Attorney's Office.
The auto theft crime referred to as "grand theft auto" is a violation of a state law. Theft of a government vehicle would be a federal offense, and prosecuted under the US laws governing theft of federal property.
There are three levels of Federal courts under the Supreme Court.
Cases fall under federal jurisdiction if they involve federal laws, the U.S. Constitution, or parties from different states. A case is considered federal if it is heard in a federal court, such as a U.S. District Court or the Supreme Court.
Supreme Court and lower federal courts
No. If the suit is over a certain dollar amount, it can be heard in federal court under diversity jurisdiction. If it involves federal law, it can also be heard in federal court under federal question jurisdiction. Unless it is a matter of exclusive federal jurisdiction, the state court maintains concurrent jurisdiction.
Supreme Court
Constitutional federal courts are either created or allowed to be created under Article III of the Constitution. For instance, federal district courts and circuit court of appeals are Constitutional federal courts. The Supreme Court also falls under the category of Constitutional Federal Courts and it is the highest court in America. Legislative federal courts, on the other hand, are established by Congress using implied power. For instance, the Court of Military Appeals is a legislative federal court.
The final authority in the federal system is the Supreme Court.
The highest court not under Federal jurisdiction would be the California State Supreme Court.
The US Court of Appeals Circuit Courts are federal appellate courts that hear appeals of cases from US District Courts under their jurisdiction. These courts are sometimes referred to in shorthand as the "Court of Appeals," so the answer is yes, under those circumstances. There is no separate federal court simply called The Court of Appeals at this time.
Yes. Patents are creations of Federal Law. Under Article III of the Constitution, Federal Court have jurisdiction to hear "all Cases, in Law and Equity, arising under ... the Laws of the United States."
A case may be appealed from a state court to the Supreme Court if it involves a federal question or if the state court's decision conflicts with federal law.