Well, I think you're both right...
Democracies will exist, in some form or another in a highly developed society. If there was no democracy to their system, the Exodus fleet would have splintered long ago and would have been swallowed by the darkness. There has to be something there or they would all be dead.
Something else that must be mentioned is that while they must have some form of democracy, they are, as a race, obviously pompous and arrogant. They are extraordinarily self-obsessed. This would of course lead to many having a lust for power, but I find their system to be more like the roman empire.
There would be one Omnipitor as I will call him and a High Council. The Omnipitor would preside over the Council. Legislation would be passed by the agreement of both. The Omnipitor's position would be passed down genetically, but should the Council "vote" him out by a very significant margin, they could replace him with one of their own. The Council would be made up of the Grand Admirals of the Exodus fleet. Each one would command their own sub-fleet. Now, of course the Omnipitor would have an elite guard (like the Mani'k), but against a unity of the Council Members, he would not stand a chance. He would have to step down or die.
Now, the way the GA's would be chosen would be by a democratic election between the captains of all ships within a fleet. By selecting one of their own, they not only stay together, but also allow individual arms of the military to function efficiently without needing the Omnipitor to do everything himself.
As for captains, there would be mutinies, but such acts of rebellion would be looked down upon. For a fleeing race, unity is crucial. Mutinies and rebellions would be frowned upon unless there was an obvious reason (ex a nutjob got the council seat) at which point it would be officially illegal, but no one would charge the rebel as they acted for the common good of the Empire.
As for the Mani'k, I do envision an elite force of ground troops that could also board starships, but I see them more as a system used as the Omnipitor's personal guard. Think of Hitler's Stormtroopers. That is what I'm thinking of here. These soldiers are the best of the best and would follow the Omnipitor's words to the letter. They would sort of act as a secret police, as they only do what they are ordered by him.
As for reproduction, it is perfectly plausible that they pull an Asguard and just clone themselves. It is also possible that they survive by turning other races into themselves (although kinda creepy...). It is also just as plausible that they do have females that perhaps give birth very rarely. This would make the life of each Vasari especially valuable and would cause the Vasari to bar females from entering military service. This would explain why the Vasari lore makes no mention of females. By taking out a "nest" of females, you could deal serious damage to the Vasari's ability to reproduce and thus fight.
As for religion, CI, you do a great job, but I think what allegiance is trying to say is that the whole suggestion that the Vasari's religion is correct (for lack of a better way of saying it) could cause some problems. Also, the Vasari's knowledge of humanity before the exodus flies in the face of the concept of the exodus! If they knew we were here, they would have avoided us at all costs. If you know there will be a road block, you pick a different route.
In general though CI, I do love your story as I have said before. You do a wondrous job of storytelling, but I think those things could be adjusted to make it even more believable/better. Keep on writing.