I know that a lot of people believe Mrs. Tredoni killed Karen. But I don't think she did. I think Alice killed Karen, and then Tredoni committed all subsequent murders/attacks.

Here's what I think:

Alice killed Karen, stole her necklace, and hid it in her basement collection. Tredoni must have known that Alice committed the murder, but may have viewed it as an act of god's will (much like how her own daughter died before her first communion). In her mind, this proved that Alice and Karen's parents were sinners, which is why she then goes after both of them. Wearing the same mask as Alice (probably in an attempt to frame her), Tredoni attacks Annie, mistaking her for the mother. Tredoni then flees through the basement, and spooks Alice, who mistakes Tredoni for the ghost of Karen. At this point, Tredoni could have snatched Karen's necklace from Alice's collection.

After Alice is taken into custody, Tredoni then attempts to frame Angela when she calls the father.

Another important detail is that Tredoni specifically attacks all of her victims with a knife, which she carries around in a bag. However, Karen was strangled and set on fire. And during her death scene, I didn't spot the bag anywhere.

The final scene with Alice also suggests something much more sinister, which I interpreted as her getting away with murder.