It's not a guessing game, exactly, but it's also not like there are hard and fast rules either. Your skill as songwriter manifests in choosing what to do.
That said, there are some useful guidelines and rules of thumb to help you think about the choices.
In my experience as music listener, musician and songwriter, I have found that composition ultimately boils down to balancing two opposing qualities: continuity and contrast.
Too much continuity (too little contrast) and the piece is ultimately boring. The easiest way to achieve continuity is to just keep repeating the same thing over and over again; it's gonna get old, no matter how good it is.
Too much contrast (too little continuity) and the piece sounds disjointed. We can get the most contrast by doing something completely different, but we risk having two or three good songs struggling to get out of one mediocre one (in other words: we have a couple of really cool sections that really don't fit together at all and would work better separately).
As applied to your question, what you'll most often want to shoot for is a chorus that is different than the verse (contrast), but connected to it in some way that is obvious to the listener (continuity). So what are our options? Let's consider some approaches:
The simplest way of achieving both a measure of contrast and continuity is to simply take the progression of one section and to transpose it to a different key - especially if we keep the riffs/motifs intact. Transposing a whole step upwards tends to work well if we want to give the whole thing more energy (the truck-driver's gear-shift), but transposing I to IV (e.g. C major to F major) or even I to V (C major to G major) also works pretty well. The transposition process is reversible, so moving from verse to chorus and back to verse is no problem at all.
If your verse is in a minor key, writing your chorus in the related major key (e.g. A minor verse/C major chorus) provides contrast (minor/major), continuity (you're still using mostly the same set of notes/chords) and an additional bit of uplift because of the "happier" character of major keys. A major verse/minor chorus might also work, though here there's a risk of the focal point of your song (chorus) being less exciting than the surrounding verses.
If you have a verse based around a repeating progression (four bars, say), you'll usually want to have it "loop" easily (that is: the last bar/chord of the progression moves back to the first bar/chord in a way that doesn't feel forced or contrived). Look at that last chord and consider: what other chords could I move to from here, without it sounding forced or contrived?
The Stephenson example in your question gives some possible answers. For example, if your verse progression starts and ends on a I, you can ask: what chords other than I would sound good approached from a I? Well, there's V, IV, vi...
Of course, we haven't forgotten that we'll need to get back to that I in the verse progression eventually, so we should write the end of our chorus progression in a way that resolves nicely to the verse.
While we're here, I would generally advise against having a section intented to contrast with the preceding one (such as verse/chorus) start on the same chord as the preceding one. Looping a single section around on the same starting/ending chord is usually ok. Staying on the same chord across sections tends to blur the section break and dull the contrast.
Sometimes having the same progression on both the verse and chorus works rather well, actually. Sometimes it feels like the best approach; the only problem being the lack of contrast. What then?
The easiest solution is to drop in a pre-chorus, bridge, interlude or whatever you want to call it. The purpose of this section isn't to stand on it's own (like the chorus or verse migh). Its purpose is to get you from point A (verse) to point B (chorus). It will often be a one-shot progression (not intended to be repeated) and you'll want it to:
start on a different chord than the verse/chorus (contrast),
end in a way that resolves well to the subsequent section (continuity).
Any of the preceding approaches may be useful here.
Regarding your second question, you're probably guessing at the answer already: when deciding how often to change chords in one section, considering what we're doing in an already existing one, we'll want to consider the balance between contrast and continuity.
Having one section be busy and another laid back, as far as the number of changes goes, is another way to provide contrast. However, we probably don't want to overdo it, lest our chorus sound like it's from a different song than the verse.
Get with the vocals (melody)
This answer wouldn't be complete without this very important part: if you have an already existing vocal line, melody or lyrics, these should be the principal guide to how the rest of the song is put together.
One thing you definitely don't want is a fight for space between your vocals and your instruments. If the vocal is carrying a busy line with lots of words, you may want a sparser harmony. If the vocal line has many long, sustained notes, you might want to mix the harmony up a bit more, to put those notes in a different light. Depending on the subject matter of the lyrics, you may wish to evoke different feelings or atmospheres with the harmony. The correct approach will depend on your pre-existing material and your imagination and taste as creator.