Zombie Jake is supposed to give you a thing you need to progress later on. You can get it from other characters, so this isn't gamebreaking, but it will prevent you from finishing the Cyseal events now.
Jake should also make another appearance at this place, so I don't know what will happen there, but supposedly you can finish the game even if you kill every NPC.
He should also have given you some more information about the murder that I'm not sure you can get anywhere else.
Spoiler text for the exact things you missed, will contain minor spoilers for the rest of the game obviously.
Jake should have told you the identity of his killer, opening up some dialog options where you can search for them. He also should have given you an amulet belonging to Evelyn which you'll need to open a barrier beneath the church. You can steal those amulets from most people associated with the Immaculates. You need to disable that barrier to finish the undead questline.
