How Did "A" Kill Karen?
Karen meets her death in the second episode, right in the middle of attempting to pull a "Carrie"-themed prank on Imogen. While Imogen is walking to the stage to accept the Spirit Queen crown, a vengeful Karen waits in the rafters, ready to dump red paint all over her former friend. There, in front of a gymnasium full of unsuspecting students, Imogen witnesses "A" push Karen to her death.
Why Did "A" Kill Karen?
It's clear "A" hates bullies, and based on the fact that they continue to threaten the Liars' mothers, they definitely believe in giving cruel perpetrators their "just desserts." This is a potential motive for killing Karen, who was a known bully at Millwood High. This isn't the only possible motive, though. Perhaps Karen saw something at the Adams house the night of Davie's death, and "A" wanted to ensure she kept quiet. Or is Sheriff Beasley (Eric Johnson) somehow implicated in Angela's death, and "A" wanted to punish him by killing his daughter? Only time will tell.