I've never played through the Dark Brotherhood quests but I know that both Nirna and Narfi are targets for assassination. What I'm wanting to know is whether or not they HAVE to be killed in order to progress the quest chain?
No. The quests given to you by Nazir are optional - although you have to complete two of them during the main Dark Brotherhood questline, you can choose which ones.
Be careful of spoilers in the General Discussion, too.