Of course, I know the Witch Cult intends to use Emilia's body as a vessel to resurrect Satella, but I wonder why? Maybe it's the fact she's a half-elf? Does the cult have other plans for her? Does the cult have some ways to contact Satella? And furthermore, did, and does, Satella agree with them?
Not revealed yet. But it could be a time travel/timeline story.
Each time Subaru dies, it’s actually a parallel timeline. Satella is Emilia from one of them... except in the future. Where Subaru did everything "right" but died.
Not knowing the truth, Emilia travelled back in time, so she can "save" Subaru from death by making him come back from death, unknowingly creating the situation leading to his death.
From the Wikia
Certain people, such as Echidna and Pandora, have referred to Emilia as "the witch's daughter", with Pandora also mentioning that she was of the witch's bloodline after seeing her power, hinting at some sort of connection between the two, though nothing has been explained.
I think that Emilia is actually the daughter of the Witch (Satella), because of three reasons :
It is mentioned many times by the villagers and other witches and many more that she is actually the witch's daughter and not the witch herself.
when she met Pandora in Echidna's tea party it felt like they both had some kind of relation (like 'aunt-niece' cause all withes are like sisters) cause Pandora was crying after they met, and she knew her mother too .
When Satella was finally revealed she had quite a uncanny resemblance to Emily like of a mother and daughter.
So at last my conclusion is that Emilia's mother was Satella and her father was some Elf and due to some cause emilia was left in Fortuna's (her father's sister) care and that'swhy even Fortuna couldn't tell Emilia 'bout her mother cause she was the witch's DAUGHTER.
As mentioned above, it is not yet revealed/confirmed, but I do suspect that this whole story has time travel written all over it. The trials set by the Witch of Greed in the Sanctuary allowed Subaru to view "An unspeakable present", there he saw all of the alternate realities where he died, all the times he died. There, we learned that people even tried healing his body and succeeded but because of his Return by Death, the Soul was no longer in his body, but instead in the new timeline where time reset.
I theorize that Satella is in fact Emilia, from the future. This can simply be an alias Emilia calls herself when she travels back in time to become the Witch of Envy. All of this, to save Subaru, who has died in her timeline. So she grants him the gift of "Return by death" after having gained enough power to do so by consuming all of the other witches. This way, she made sure Subaru would live no matter what, in one timeline. This would explain why Emilia looks IDENTICAL to Satella, why she gave the name of Satella in the first episode, why Satella is OBSESSED with Subaru, and claims to love him deeply. She obviously knows him, but he doesn't know Satella. This is because, as I mentioned, Satella is definitely a future Emilia from another timeline. Time travel is confusing ;D
I feel as if Satella is actually Emilia, who travelled back in time to get the authority of Envy but suddenly got trapped in the past but somehow had a link to Subaru and her present/future events. Which could explain why she knew about Subaru before he came to Lugnica and why Emilia gave herself the name of the Witch of Envy. It would also explain why their appearances look similar because Satella looks similar to an adult Emilia which could explain why she was able to retain knowledge about Subaru. She even acted on “love” and brought him to Lugnica and cursed him with Return By Death so that he could create a future where they could be together.