My theory is that Emilia was made by Satella as a reborn version of her that has the same personality but one which can avoid the circumstances that led to collecting all the witch factors.

Emilia used to live in a village guarded by the witch cult, meaning she is chosen by the witch cult somehow. Even as a kid she has incredible magical power.

This would also solve how she is the daughter of a witch and explain her half elf heritage. She is Satella's (half elf) "daughter", and there was no 2nd parent.

Several times we've seen that under certain circumstances Emilia can become straight up similar to Satella. If Emilia is given proper support, she becomes a mature and all loving heroine, if she doesn't, she becomes a selfish and destructive yandere.