Blood-chillingly creepy, disturbed Eerie Pale-Skinned Brunette 10-year old European orphan who causes horrible things to happen to kids around them? Sounds familiar. Saarne Institute is, in fact, a wizarding prison disguised as a mental hospital to fool Muggles. Once Leena Klammer, the greatest Dark Witch who ever lived, managed to escape them, her only means of hiding without recognition was to be adopted by a Muggle family, since the entire wizarding world knows her face.
Esther is Henry Evans' daughterForget Evans falling off the cliff, lets assume that somehow he survived, fled to russia, knocked up some woman, then years later Mark found him and killed him, resulting in Esther being an orphan,
Esther is Wednesday AddamsEsther was previously adopted by the Addams family (using a different false name and disguising her accent, naturally), but was unable to carry out her usual seduction-and-killing plan because the Addams family took her sociopathic behaviour in stride.
Esther was punishing Kate specifically.Although Esther was trying to seduce John, there are moments in the film where it comes off as though Esther is enacting her own twisted version of justice on Kate- she confronts Kate with how Max nearly died because of her drinking and tells Kate she's taken her family for granted. The more Kate lashed out at her family for not believing her, the more Esther was convinced that Kate (and Danny, by proxy) deserved to be punished. Her affection for Max dwindled when Max proved more loyal to Kate than her, which is why she turned on Max after John rejected her.