What criminal cases are heard at superior courts?

Yes. Charges of federal crimes are heard in federal criminal court.Yes, providing that they are cases that involve violation of federal criminal law.

It depends on what the various states call their mid-level state court system. "Circuit Court" - Superior Court" - "District Court."

California Superior courts hear all cases where one or more of the crimes charged is a felony. Per California Penal Code section 17, a felony is defined as a crime, where if the defenadant is found...

Generally, cases are first heard in whatever trial court has original jurisdiction over the case depending on the laws, territory and/or special subject-matter involved.

All cases (both criminal or civil) having to do with the violation of laws promulgated by that state's Legislature.