First of all, I primarily want to talk about the subject, not necessarily just to find the answers. You could for example write about a hypothetical empire (how you would model it to work) or what kind of empire you would like to run as a player, things like that. The questions were just to start the discussion.
look at past empire
I have trouble locating any real emperors in our history which were stable (long run). On Earth in the middle ages there was everywhere a feudal system (not an absolute monarchy) and basicly the moment it turned into absolute monarchy all these persihed (French revolution, and all that follows), note that only monarchies that did not turn into an absolute monarchies survived (like in England). It simply seems that the most tasty (from the storytelling point of view) imperial goverment systems simply do not work too well in a long run... Not that we need to make it that realistic, but still.
The only situation when an absolute (or nearly absolute) rule woudl work i can think of is war or tother big danger. The "dictator" was a title invented by Romans in the time of deadly barbarian threat to their empire. It seems that only a big danger makes people willing to bestow huge power into the hands of one individual.
Why would they overthrow him? An emperor is not always bad except for the other countries.
Exactly, oppressive regime can only go so far. In the end there must be some benefit to majority of the population (or at least to the majority of the most rich/influential people). The question is, what is so benefitial in a strong imperial system?
Why it can't revert to democracy? Same as above, why would they do that? Is democracy the bestest solution?
Well, here I have a problem. So far it has been proven that democratic system is the best In Poland not that long ago we overthrow communist system and installed capitalistic democracy, the comparison in overall wealth and well being of everyone (even the poor workers abused by big corporations who think only about profits) is soo huge in favour of democracy that there is nothing to compare.
Note that it is about our current times (and technological level and transport capabilities), in medieval times a feudal system seems much more efficient.
Same for slavery, it persihed the moment it became unfeasible (machines required educated workers and steam engines that made physical strength during production process unimportant).
The thing is, we need to invent some circumstances when an imperial system is the best solution.
What are the imperial institutions? The same existing nowadays I presume. Plus the one responsible for the propagenda.
Well, I'm not sure it sould very appealing Probably realistic but not appelaing At least these should be somehow named differently.
Bonus : You can also have some sort of psyonic entity as en emperor. And you can start with this to answer all the previous question.
LOL, a dirty cheat. Yet it solves all possible problems indeed