The US Court of Appeals Circuit Courts only review cases under their appellate jurisdiction; the US Supreme Court hears most of the cases it selects under appellate jurisdiction, but considers...
In many states they are the Circuit courts. In some they are the Superior Courts. In New York state it is the Supreme Court. In the federal system it is the US District Court for most matters.
No, an appeals court hears arguments that there was something wrong with the way a trial was conducted; if there was an error the case goes back to trial. A trial court hears testimony and decides...