So... is Final Fantasy: Unlimited finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Final Fantasy: Unlimited follows the journey of twins, Ai and Yu Hayakawa, as they search for their missing parents. Their parents, renowned scientists Joe and Marie, disappeared twelve years after a strange interdimensional event. This event involved the appearance of monstrous beings over the Sea of Japan and their subsequent battle.
Driven by the mystery of their parents' disappearance and the world they researched, the twins embark on a perilous adventure to find them. They seek entry to this mysterious dimension, inspired by their parents' legendary book, "Day of Succession."
Their quest begins in an abandoned subway station, where they encounter Lisa Pacifist, who becomes an unexpected ally. Together, the three travel to this unknown world to unravel the secrets of Wonderland and locate Joe and Marie Hayakawa. Their journey is fraught with uncertainty, as they venture into a realm beyond comprehension in search of their family.