Short answers, pulled from the story.
The Atrium Libertatis was a multipurpose administrative structure in ancient Rome, primarily serving as the seat of the censors' archive. It held official lists of Roman citizens and bronze tables engraved with maps of the ager publicus, the public lands. The complex also included two libraries and possibly a basilica known as the Basilica Asinia.
The Atrium Libertatis stood on the saddle connecting the Capitolium to the Quirinal Hill, a short distance from the Roman Forum. This ridge placed it at a strategic point between two of Rome's most prominent heights.
The building was rebuilt at least twice. The censors of 194 BC oversaw one reconstruction. Gaius Asinius Pollio then funded a second complete reconstruction starting in 39 BC, using spoils from his victory over the Illyrians, with the full complex intended for completion by 28 BC.
The complex contained works by sculptors from two traditions: the refined Neo-Attic style and the more dramatic Anatolian school. Among the most celebrated was the Supplice of Dirce, attributed to Apollonius and Tauriscus. The sculptor Stephanos's group called the Appiadi was also displayed there, mentioned by the poet Ovid in connection with the neighboring Temple of Venus Genetrix.
The building was demolished at the beginning of the second century to clear ground for the Forum of Trajan. The mountain saddle on which it stood was deliberately leveled as part of that construction project.
The Basilica Ulpia and the two libraries beside Trajan's Column took over the functions of the older complex. The ceremony of freeing slaves, an act directly evoked by the building's name, probably moved to one of the apses of the Basilica Ulpia.