Short answers, pulled from the story.
An appellate court, commonly called a court of appeal or second instance court, is any court empowered to hear a case upon appeal from a trial court. This definition distinguishes it sharply from the trial tribunal that initially hears cases and considers factual evidence.
In common law jurisdictions, an appellate court reviewing an issue of fact ordinarily gives deference to the trial court's findings. When reviewing lower decisions on an issue of fact, courts of appeal generally look for clear error rather than retrying the facts themselves based on the evidence already in the record.
Texas and Oklahoma have the final determination of criminal cases vested in their respective courts of criminal appeals. Alabama and Tennessee allow decisions of its court of criminal appeals to be finally appealed to the state supreme court.
Historically, England and Wales had a Court of Criminal Appeal that was abolished in 1966. Ireland also maintained a Court of Criminal Appeal until it was abolished in 2014.
Judges in the Scottish Court of Session are termed Lords of Council and Session and appointed simultaneously to the College of Justice. Their number is fixed by statute currently at 37, though temporary judges assist with workload.