There are three types of ecclesiastical penalties: excommunication, suspension, and interdict.
The Apostolic Penitentiary is a tribunal which deals with reserved cases of excommunication (latæ sententiæ), reserved impediments, governance of indulgences, and issuance of indulgences.
The Roman Rota is the highest appellate tribunal of the Catholic Church. An appeal of a sentence is made to the ordinary appellate tribunal or to Roman Rota.[FONT=garamond][FONT=garamond]
A decision can normally be appealed. I don’t know if they can always be appealed.
Once a cause for nullity has received two affirmative decisions, there is freedom to marry.