There should be no essential NPCs at all.

I think you should be able to kill everyone in the game. If the person you kill or dies randomly would have been necessary for a quest, the quest fails immediately. But I think quests should have different ways of completing to avoid this.

For quests that are very important, like part of the main quest or which give unique rewards, you should be able to talk to the relevant people even if they're dead. This is Elder Scrolls, spaking with the dead is not that difficult. Either have their ghosts wandering around or have some midly difficult way to invoke their sprits via necromancy or conjuration.