1.
inversion : see
this thread
This is the case of an "incise", a clause added between two commas or at the end of a sentence, to mention who is speaking or to make a remark which interrupt the story.
"J'ai faim, dit-il, en se dirigeant vers la cuisine".
"C'est moi qui ai mangé le chocolat, avoua-t-il".
"Il exagère, pensais-je, il n'est pas tout seul !"
The inversion is mandatory, here.
2.
tenses :
I assume you're speaking about :
ai-je cru comprendre
The author chose the passé composé. The story is told in present, as you saw, to make the narration more vivid, but when he makes his own remark, this one is
not in the story and he reports it in the true tense when he made it : the past.
Another example : when he says
"moins modeste que je ne l'aurais supposé" he uses the "conditionnel passé".
- conditionnel, because he expresses an hypothesis,
- passé, because, obviously, as in the first case, this personal comment takes place in the past, not at the moment when he tells the story. It's only a retrospective hypothesis. At the moment, he knows the house is larger than he thought.
"J'aurais supposé que sa maison était plus modeste, mais elle ne l'était pas, elle était moins modeste" = I would have assumed that... but it was not.
Does it help ?
Jann was quicker than me ! She tells the inversion is a choice... I don't think so, imo, it's mandatory here.