1. What is the timeline of the Empire, and how does it fall? Here's what I have:
The Old Empire is established.
Time passes.
The cult of necrosavants forms in the southern part of the empire.
The last Emperor's child is stillborn. He and the empress make a pact with an "ugly man" (a necrosavant) to ensure that their empire lives forever, with them as the rulers. It requires blood from them and their child, and has the side effect of making the Empress barren.
Time passes.
The emperor claims to be the chosen one who will defeat death.
There's a disaster of some sort in the capital, described in the initial undead crisis vision as resembling an volcanic eruption, though possibly it's magical and somewhat intentional. (The Empress points at the assembled legions and says they are going to defeat death itself beforehand.) It doesn't seem like everyone who died was on board with the plan.
2. Why does the undead invasion begin and end?
Based on your visions, the invasion ends when the woman in them no longer wishes to prosecute it. (Reasons: either because she knows the emperor is not the chosen one, because you ask her to, or because she turns her anger toward the Ugly Man responsible for the creation of the ancient dead.) This might mean she was the motivating force behind it to begin with.
Okay, but why does she start the invasion in the current time, after being dead for hundreds of years?
3. What is the mercenary captain's connection to the undead? / Who is the False King?
There's some indication that the ancient undead have not been active for very long; i.e., when you encounter them, the narrative segments describe them as an unfamiliar enemy. No other opponents in the world are described that way, hence they probably haven't been active for long.
The undead seem to think the captain is someone important, although the woman and the undead armies may disagree about which person that is.
The empress clearly thinks the captain is the emperor. (Why?) If she's right, what's the mechanic? (Reincarnation, distant descendant, superficial resemblance?) If the captain isn't the emperor, what has the emperor been doing during the invasion?
The other undead seem to also regard the captain as being special, based on how they apparently are interested in killing him specifically on various artifact retrieval missions. Strange behavior if they also think you are the emperor, since he would presumably share the empress's ability to control them. Maybe you just resemble him, and thus you inspire their resentment but not their obedience? But there's still no explanation of why they call you the False King rather than the False Emperor, unless it's a sassy aristocratic insult.
Also, one of their two lines is that "the false king must die," spoke immediately before trying to kill you. Occasionally the artifact you are given to retrieve is the Seal of the False King, so clearly this personage has some presence in their culture predating you, or indeed the fall of the empire. Do they think you are this person? Why do they react so differently to you than the empress does? It doesn't seem like this is plausibly a case of two different perspectives on the same person, but rather that they believe you to be two different people. Maybe the False King was a rebellious vassal of the emperor who they fought before the disaster that ended the empire, and since the captain is leading the fight against the undead (as far as they know), they identify one with the other?
Possible explanations:
The captain resembles the emperor. Early game tomb raids wake up some portion of the undead, who wake up the rest, including the empress, who mistakes the captain for the emperor risen again, who sends his legions to his lands to reconquer them for him. Fighting against the undead gives the appearance that he has forsaken them, which leads to the empress stopping the invasion.
The woman in your visions isn't actually the empress. She's a symbolic representation of the old empire, and acts as their collective consciousness in undeath. Hence the significance of making her "barren" via the pact with the ugly man as a metaphor for turning the empire undead.
4. What role do the necrobros have in this?
Based on the event you sometimes get if a city falls to the scourge, a dude first appears to you as a pale old greybeard, refers to "the ones you call necromancers," and claims to have orchestrated the demise of the city before turning into a cloud of bats and flying away. So, he first looks like a necromancer, then he manifests powers exclusively possessed by necrosavants.
Based on this, the necrosavants appear to be sapient and involved in the leadership of the undead armies, and the necromancers seem to be proto-necrosavants. Based on some missions, the necromancers also seem to be playing a role in stealing artifacts of the old empire from towns. Are they manipulating the scourge?