My personal theory:
I dont know much about ghosts or curses or something, but... what if, when Eddas ghost is actually some kind of manifestation of her wish to be reunited with her dead fiacne Avere. To do so, she still need the soul/body of an adventure. That means, her ghost is seperated from her soul and her actual body, but still have some kind of own personality. Its more like a wandering presence, haunting other adventures for their souls/bodies to make her wish come true.
Now back to Eorzea. As far as we know, Bahamut is a primal. Primals were just fanciful imitations of the originals.
Bahamut was one of the great wyrms. During the Third Astral Era Bahamut fell to the invasion of the Allagan Empire under the reborn Emperor Xande. In her grief, Tiamat was manipulated by the Ascians into summoning him back as a primal—something she quickly regretted as the Dreadwyrm was nothing but a crude imitation of the original Bahamut.
So, what if Eddas ghost is a primal? An imitation of the original Edda? A manifestation of her feelings (dispair, sadness, madness), as we killed her fiance at the end of Tam Tara HM?
It sounds weird, but it would explain why her ghost and her (real) appearance in the palace of the dead is so different to each other. It would explain, why you dont need to finish Tam Tara HM first, before entering the Deep Dungeon. It would explain, why she is mentioned as "Edda Blackbosom" and not as "Edda Pureheart" in the 50th floor. And maybe her ghost will still appear in the big city states, even after you defeated her body in palace of the dead.
Could it be Paiyo Reiyo (a wizard?) who ressurected Eddas body? What do you think?
There is one thing that still bothers me:
Let me say, you re new with A Realm Reborn.
1. You met Edda before entering Sastasha Normal (your very first dungeon). Everyone is alive.
2. You met Edda (and her group) after Tam Tara Normal, Avere is dead.
3. You met Edda alone after Copperbell Mines Normal, where she want to start a new life.
4. You met Edda in the 50th floor of the Palace of the Dead and defeat her. She is dead, right?
BUT: 5. You met Edda again (but more lunatic and mad) in Tam Tara HM, including her creation: Voidsent-Avere. After that: Her ghost shows up.
How is this possible?