Short answers, pulled from the story.
An appeal is the legal process in which a case or decision is reviewed by a higher authority, where parties formally request a change to an official decision. Appeals serve two purposes: correcting errors made by lower courts and clarifying or interpreting the law for future cases.
Common law countries did not incorporate an affirmative right to appeal into their jurisprudence until the 19th century. England moved civil cases to a proper appeals system in 1873 and extended that right to criminal cases in 1907.
Appellate courts trace back at least to the first dynasty of Babylon, when Hammurabi and his governors served as the highest appellate courts of the land. Ancient Roman law also recognized the right to appeal in the Valerian and Porcian laws since 509 BC.
Hikitsuke was a high appellate court established by the Kamakura shogunate in Japan, which ruled from 1185 to 1333. It was created to help the state adjudicate an accumulating body of lawsuits.
In American courts, a case goes "on appeal" and is resolved with language like "judgment affirmed" or "judgment reversed." British courts say a decision is "under appeal," parties "appeal against" a judgment, and outcomes are described as the appeal being "dismissed" or "allowed."
Yes. In the United States, litigants may waive the right to appeal, provided the waiver is considered and intelligent. Most jurisdictions recognize this right can be given up voluntarily under those conditions.