is there a difference or nuance between Αυτός πηγαίνει, Αυτός πάει or are they completely interchangeable as the exercise suggests?
They are interchangeable in present tense only. In other tenses, πάω shows momentary movement, whereas πηγαίνω continuous. Pe: θα πάω- I will go. Θα πηγαίνω -I will be going.
I think the difference is in what we call in czech "slovesný vid" (eng. grammatical aspect, you can read more about it here https://en.m.wikipedia.org/wiki/Grammatical_aspect) We have this for almost every verb. But if if use this example: "jdu"=πάω vs. "chodím"= πηγαίνω. The latter indicates either a continous or habitual action. In other tenses there is also a visible distincion of perfect vs. imperfect. Pretty much where other languages use different tenses we use different verbs which mean rhe same thing. It is quite complicated. As far as I know it is that common in Greek, I cannot think of another example right now.. I hope I didn't make it more confusing!