The US Supreme Court can only review cases on appeal from, or when an appeal has been refused by, a state's "court of last resort" (usually called [state name] supreme court, but there are...
In order to have an appeal heard by the Supreme Court, a person must file a "petition for a writ of certiorari," asking the Court to review a case and issue an order, called a writ of certiorari, to...
According to Law.com, approximately 16% of the US Supreme Court's docket are cases on appeal from state courts; this represents approximately .8% of the cases petitioned to the Court.
No. The US Supreme Court is the final appellate court for cases heard under its jurisdiction; their authority supersedes that of the state supreme courts.