I'm still trying to complete it, and I'm not sure about this thing - when I activate the artifact, does it hurt Kerrigen?
It definitely hurts her, but doesn't kill her (if she has full HP). I believe that the artifact does 800 dmg to anything in its radius. If I recall correctly, Kerrigan has 2500 HP.
The main use of the artifact in this mission is to clear the area around your base of enemy forces. Even if Kerrigan survives the blast, your own troops will make short work of her since there'll be nothing else to shoot at.