That would be the process by which you select your leaders. Not too different from a democratic republic. It does not mean every single one of them understands the inner thoughts of those leaders, though. It’s a selection process. Does a selection process give you the power to understand their secret minds, or do you simply think they have no secrets?
Yes, national power is exactly what we’re talking about. Exercising it over a broad area, of people who did not before fall under your control, is empire-building. Or, imperialism. Power + new lands/people = imperialism.
Hegemony simply refers to degree of competition. If an empire is contested by near-peers, it does not have hegemonic control. This is core to what the word means in the English language.
I appreciate the sources, but if you as a believer cannot adequately explain these things from them, I’m not sure the sources will be of much benefit.