We don't know who XII!Cuchulainn is yet because he's likely going to be someone in Zadnor and that doesn't release until 5.55. However, the Espers/Lucavi seem to be creations held inside Auracite, much like the Primals were in the Thirteenth, with the Auracite's power, and people can also turn into such beings, such as Argath and Ba'Gamnan and, later, Albeleo (from a completely different Matsuno series, by the way!)

Ultima, however, seems to be an alien being who descended upon Hydaelin, more like JENOVA from FF7. However, she was trapped in the Virgo Auracite by Ramza Beoulve. Other than that, however, I'd have to replay the quests.