Re. points 1 and 2: These characters appeared about 3000 years ago, and there are few primary sources from that time. So it is hard to tell how exactly such banners would have looked or what would have been depicted or written on them.
Re. points 3 and 4: yes, this would be hard and not really productive, but that might be part of the point? That you can have a servant who holds a banner with a job description like "Important boss who will make the peasants work"? There are actual (though much more recent) depictions of people doing similar kind of work, i.e. holding stuff up for people far above them in social hierarchy. Therefore, someone holding a banner for an official does not sound implausible at all.
Another great source of depictions with people holding things to make their bosses look more prestigious are the Ming and Qing era versions of the "Along the river during the Qingming festival" paintings. In the Song era version it is not so apparent for some reason. However, keep in mind that these are only 300 to 500 years old. In European terms that would be like using paintings from 17th century Greece to illustrate points about the Mycaenean civilation. But I think they can be used to prove a general point: If you are high enough in the hierarchy, you can have people doing stuff that serves no real purpose except representation.
From one of the Ming era versions:
From one of the Qing era versions:
One particularly striking example is from the same Ming dynasty version as above, but (I am guessing) seems to involve foreigners rather than an official:
That said, Chinese internet sources usually give a different explanation for that character: that it depicts a hand holding a hunting net (for hunting birds maybe?), and that the character originally meant "to hunt". According to these sources, the meaning of "to administer" only came later.
Chinese characters acquiring a new and unrelated meaning is actually not that rare. One well-known example is 象, which originally means elephant, but because being pronounced exactly as 像 has taken a lot of that other character's meaning (i.e. "shape" or "to resemble").