Verb conjugation and reflexive pronoun usage aren't the issue here. French reflexive pronouns are similar to the English word self, as in Je me lave -- I wash myself, although in English we don't always spell it out as carefully as the French do. French requires the reflexive pronoun, but in English the self is often understood.
The two examples at the end of the lesson are the confusing part. The first example gives the reflexive structure as the non-idiomatic -- Nous nous demandons, but the second example gives the reflexive structure as the idiomatic -- Il s’installe. It seems to me that either the idiomatic or the non-idiomatic should have the reflexive pronoun, and it shouldn't be switchable -- little wonder I'm confused.