Past - set fiction. It's a very straightforward way of referring to fiction that is set in the past. It doesn't specify a particular era or type of historical event, but simply indicates that the story takes place in a time that has already passed.
Antiquarian fiction. This term is not as commonly used as the others, but it refers to fiction that has a strong focus on antiquity or ancient history. It might involve elements such as ancient civilizations, their cultures, and their myths.
Sure. One synonym is 'past - set stories'.
Yes, 'root story' can also be considered as a synonym for origin story. Consider a cultural tradition, its root story would be the one that details how that tradition started, what the initial circumstances were, and how it has evolved over time. It gives a fundamental understanding of the origin of that cultural element.
Sure. 'Traditional stories', 'heritage tales' and 'legacy stories' are also synonyms for old stories.
Sure. 'Haunting story' is one. It gives the idea that the story will stay with you, like a haunting. 'Nightmare story' is also a synonym as horror stories can be like nightmares.
Scare stories, hair - raising stories.
Yes, there are also 'celebrated novel', 'esteemed fictional work' and 'memorable story'. A 'celebrated novel' is one that is widely known and praised. 'Esteemed fictional work' indicates that it is held in high regard in the literary community. And a 'memorable story' is something that readers can't easily forget, which is often true for classic novels as they usually have very engaging plots and characters.
Success sagas, winning yarns.