More specifically, I'd be interested to know if the average person, or even subsets within civilizations with imperial cults were in awe of their ruler and/or thought that he/she possessed supernatural powers.
Or, were they more like, "Yeah he's a pretty damned important guy and he's doing a good job of keeping us safe. Also, he said that he's a god and that if we finish his pyramid before he dies he'll keep protecting us from the afterlife"?
Lastly, and kind of tangentially, was is there any consensus on whether Alexander the Great claimed to be a god (or at least demi-god) during his lifetime?
Sadly, we have no Egyptian philosophical texts that I'm aware of that might shed light on this matter.
There is some difficulty in addressing this question specifically because the span if history you're talking about is so huge. We know that initially the Pharaoh was a high priest who's duty was to go around to all the major temples performing ceremonies. Later this role was delegated, although the Pharaoh still retained his title as high priest of all the gods. Later on the role fluctuated depending on the strength of the guy in power...just remember that you're talking about more than 3,000 years of Pharaohs.
Difficulty is, we have basically no written records from Average Djoset Egyptian. We don't really KNOW what they thought, or even have any sort of hint of it. We do have the official religious documents, which vary from era to era. But these don't really give us any idea as to what the common people thought.
Given the Pharaoh's authority, though, I would expect that there would generally be plenty of bowing and scraping, since he would undoubtedly have priests/guards/courtiers to make you bow and scrape if you tried to avoid doing such. Some of the probably were quite capable of enforcing royal etiquette on their own, of course, since the early Pharaohs were expected to lead the charge in battle.
As to Alexander, he claimed to be the son of several gods. Zeus and Amun (later combined into Zeus-Ammon under the Ptolemies,) being the most famous.