Mfcttrf

I've been solving exercices in a book called practice makes perfect (linked down below)
And in the Plus-que parfait exercices (page 82,81. 10.2 Exercice. N.3, N.10) there are those two sentences which are really confusing me :

Tu (se demander) ....... s'il était allergique.
Elles (s'écrire) ..... pendant des années.

The answers ,according to the Answer Key, should be (t'etais demandé(e), s'étaient écrites) but I don't understand why there is an agreement here. I thought that reciprocal verbs which take an indirect object its past participle does not agree with the subject. And worth noting also that in the exercices of the Passe Composé there are those two similar sentence which have no agreement (page 63) :

Ils se sont écrit de long lettres.
Nous nous sommes demandé pourquoi il était absent.

And here's a part of the book explanation for the past participle agreement thing (page 62,63) :

"When reciprocal verbs take an indirect object in French, the past participle does not agree.

Ils se sont téléphoné. They called each other.

Vous vous êtes parlé au téléphone. You talked to each other on the phone.

Ils se sont écrit de longues lettres. They wrote each other long letters."

Book link : ( https://archive.org/details/practice-makes-perfect-complete-french-grammar/page/n94 )

Note : please don't explain in french. My french isn't that advanced yet and it will be super hard to understand it.

You are right, there shouldn't be an agreement.

As you can see, both t' and s' are indirect objects here : to whom did you ask etc.? to whom did they write ? etc.

As per the rule you quoted near the end of your post, when reciprocal verbs take an indirect object, the past participle does not agree.

Therefore it should be:

Tu t'étais demandé s'il était allergique.

Elles s'étaient écrit pendant des années.

The agreement in the case of "tu étais réveillé(e)" for example depends on the sex of the person who is talking/whose you are talking to (the subject). There is no indirect object here. It is a simple agreement like "tu es intelligente" when you are saying that to a girl.

The agreement in "elles s'étaient écrites pendant des années" (and so "tu t'étais demandé s'il était allergique" is different, because you can say "à qui / à quoi / de qui / …" after the object that means it is an indirect object. And in that case indeed the past participle never agrees, even with "être". As you may know, past participle agrees when "être" but not "avoir" in the case of a direct object.