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.