La inquisición española:
(1) comenzó en España en 1478 - correct
It was founded in 1478 by the Catholic Monarchs (Reyes Católicos), Queen Isabella I of Castile and King Ferdinand II of Aragon. This kind of institution existed before in France, but it officially began in Spain in 1478.
(2) se estableció para crear una unidad religiosa - correct
The main purpose of this public organ was to maintain the catholic religion strong, big and avoid paganism and heresy.
(3) torturar era común - correct
Torturing was the most powerful arm of the Inquisition. The accused individuals were subjected to many kinds of torture, some of them were even invented by the Inquisition itself.
(4) el Palacio de la Inquisición fue construido en Cartagena en 1610 - incorrect
This building was the Inquisition's court. It was constructed in Cartagena, Colombia, but in 1770, not in 1610.
(5) se creó para evitar las conversiones al catolicismo - incorrect
The institution of Inquisition worked on converting Jews, Protestants, Muslims, etc. to Christianity. Many of them saved their lives by giving up their religion and changing to a Catholic.