Idiomatic and Non-idiomatic Pronominal Verbs

Lesson 10.5 presents pronominal verbs, and at the end of the lesson are idiomatic and non-idiomatic pronominal verbs.  Two examples are included.

First example:  Idiomatic:  Je demande à Céline son adresse
. . . . . Non-idiomatic:  Nous nous demandons où ils sont

Second example:  Idiomatic:  Il s’installe dans sa nouvelle maison
. . . . . Non-idiomatic:  Elle installe la nouvelle télévision 

One example appears to be in error, and I think it's the first one, but I'm not sure -- I'm confused.

Hi Diana-S1, the examples are good. Keep in mind that you will end up with a «nous nous» or a «vous vous» in the case of pronominals or reflexives.

The first example is demander (à qqn) = to ask (someone) versus se demander = to wonder {in a reflexive sense, to ask oneself}. Note, you don't add the à to se demander  since you're not really "communicating" with someone else.

So the present tense conjugations are:
je me demande
tu te demandes
il/elle/on se demande
nous nous demandons
vous vous demandez
ils/elles se demandent

Je demande à Jean la direction. / Je lui demande la direction. = I ask Jean for directions / I ask him for directions.
Jean se demande s'il est perdu. / Il se demande s'il est perdu. = Jean wonders if he is lost. / He wonders if he is lost.

The second example is installer = to install versus s'installer (dans) = to get settled into

Present tense conjugation:
je m'installe
tu t'installes
il/elle/on s'installe
nous nous installons
vous vous installez
ils/elles s'installent

Nous installons des étagères dans la chambre. = We are installing/install some shelves in the bedroom.
Nous nous installons dans un nouvel appartement pour l'hiver. = We are settling/settle into a new apartment for the winter.

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.
   

Ah, okay. You're right, I think it's because the examples aren't really that idiomatic. You can arrive at the same intent by applying the "self" rule as you mentioned with Je lave la vaisselle and Je me lave.  The "standard" and reflexive versions aren't vastly different.

A better example would have been faire (to do) versus se faire à (to get used to), since there's no way to deduce the second by adding "oneself" to "to do".