The correct answers are People used to believe a ghost lived in the attic. and The mansion used to belong to a wealthy pirate.

"Used to" is perfect for describing past states (like "believe" or "belong") that are no longer true.

We cannot use "would" for past states (only for past repeated actions). Additionally, "was used to" means "was accustomed to," which doesn't fit here and requires an -ing verb anyway!