I think the idea of its just Random citizens applies to the majority of the imperium's military. Unless you are working in that area of operation directly, you are probably clueless as to what is happening. If your working adjacent to it you probably have some idea "oh those guys with the purple eyes are fighting monsters and other heretics.".
Yes and no. You also need to consider than the imperium uses muster worlds where regiments from all sorts of planets... muster(that's kind of self explanatory) as well as the imperial navy who has to cart the guardsmen around. No, I'm not going to count imperial military forces as being the equivalent of random civilians. The reason for this would be that generally xenos knowledge other than "alien bad" barely exists, however the Infantryman's Uplifting Primer definitely covers how to fight xenos and every guardsman has one(or should). On top of the navy, even civilian transport services(bulk freight haulers and such) have been used to move guardsmen around, and of course aid the Munitorum in logistics(food and such, not actual arms) when necessary, which again exposes more people to information. And this is all of course ignoring the mechanicus who are kind of isolated by way of not speaking gothic regularly, but also have members definitely aware that daemons and other warp fuckery exists.
There is definitely no way Cadia and her people aren't fully aware of the situation after fighting it for the last 10,000 years.
The modern Cadians would have only been fighting for a few thousand due to that purge of the original population bit(it's where Lorgar killed some custodes and maybe made some gal vorbak?)
Citizens arent free to move about, the entire universe operates on a feudal system at a macro level. The vast majority of people will never step aboard a space craft and those that do will never step off it. Word of mouth does not travel far.
They actually mostly are, and some do all the time. See the previously mentioned guard units, muster worlds, and imperial navy. The difficulty is being able to afford it, but generally speaking there's nothing stopping civilians from finding a way to travel from one imperial world to another. Some planets have visa systems even for workers.
The thing about propaganda is that it's a lie. One man's retardation could be a propagandist's story of self sacrifice and heroism.
Sure, if you want to pull the unreliable narrator bit with Krieg, except that's never even hinted at as being propaganda. But the problem is that wouldn't make sense even within 40k because it would be making up a lie about a rebellion... which the imperium wouldn't have a reason to do(why would the imperium include a public history of open revolt as a source of pride in anything?), not to mention Krieg became a deathworld by nuking themselves during their civil war.
Sure, but at this point most of this stuff if 15-20 years old but even then you've still got multiple loyalist space marine chapters basically in a cold war with the inquisition, which keeps the reach of the inquisition limited in ways(and of course not all of the ordos even give a shit if someone knows about daemons, it's just most likely that a witness wouldn't survive whatever happened to begin with). Then consider shit like flects specifically causing warp related issues among the civilian population leading PDFs, arbites, and so on to have to deal with it as well. The point being, that the imperium is such a mess, it can't keep up with the "lets just mind wipe or kill everyone" approach due to internal conflict and lack of resources, especially with the Eye of Terror having blown up into the Cicatrix Maledictum cutting off half of the imperium from Terra leaving xenos, traitors, and daemons with them running amok.