Short answers, pulled from the story.
A Roman governor served as the province's chief judge and held the sole right to impose capital punishment on those accused of crimes within his jurisdiction. Capital cases were normally tried before him alone in the provincial court.
To appeal a governor's decision required travelling all the way to Rome and presenting one's case before either the praetor urbanus or even the Emperor himself. This process was expensive and thus rare for most citizens, and an appeal was unlikely to succeed since a governor would not generally take the chance of convicting someone contrary to the Emperor's wishes.
During the era of the Roman Republic the council was in charge of appointing governors to Rome's provinces. This was done by appointing promagistrates to serve either by random casting of lots or by senatus consultum which meant advice of the Senate.
Under the Dominate the Emperor Diocletian began in AD 293 reforms of the provincial administration that were completed under the Emperor Constantine the Great in 318. These reforms included setting up twelve dioceses later several were split originally two to four for each of the four co-emperors under the short-lived Tetrarchy.