Page 115
The core action (verb) of the sentence is 赤面する, essentially “to blush” or “to be embarrassed”.
Adding the causutive helper verb (さ)せる changes this to 赤面させる. This means to cause someone to blush, or to be embarrassed. Note that it doesn’t necessarily mean that they are making someone be embarrassed. They’re just responsible for that outcome. If the effect is Urushi being embarrassed, the cause is whatever situation Ayumu created.
Finally, added to this is the receptive helper verb (ら)れる (which often gets called “passive conjugation”, a double misnomer to confuse people learning Japanese). This means the subject is receiving the action of the verb. Here, Urushi is receiving the action of being “caused (by Ayumu) to be embarrassed”.
Verbs with a receptive helper verb attached tend not to translate cleanly to English. (And English textbooks often muddy the waters by making the English translation into a passive sentence rather than active.)
Verbs with a causitive helper verb attached often have their meaning slightly changed when translating to English, due to limitations/difference in the concept in English versus Japanese. (But this is the case for a lot of things, due to how different the two languages are.)
If I were aiming to translate this sentence in a way where I tried to capture the meaning of the Japanese, even if it makes the English sound awkward, I would go with:
“For the amount I’m always getting made to be embarrassed (by Ayumu), I’ll take revenge on him.”
The English “let’s” is typically used to translate the Japanese volitional (intention to do something), which in this case would be 「やろう」. Granted, my translation (“I will”) is also a form of volition in English.
The first sentence is essentially two sentences combined with が:
「何か知らない」 => 「なんか知らん」 “(It is) something not known.”
「が」 “but”
「チャンス」 “(it is) a chance/an opportunity”
Essentially, she doesn’t know why he’s blushing, but she sees an opportunity.
I might translate this loosely as:
“I don’t really get it, but this is an opportunity! I’ll get even for him always causing me to be embarrassed!”
Page 120
Long sentences can definitely be difficult. But once you account for which words/clauses modify which nouns, it isn’t quite so bad.
I read this で as the て form of だ, so the modifier on “that Ayumu” I translate as, “(that Ayumu who) was blunt and was interested in nothing but kendo”. (Compare that former blunt-Ayumu with the present concealing-his-feelings Ayumu.)
The ん here is a colloquial form of の. This のだ is the explanatory form.
What this does is take a sentence, turn it into a noun, and present it as a noun sentence:
“It is (that) [sentence as noun].”
Saying, “Ayumu is in love,” is stating a fact.
Saying, “It is that Ayumu is in love,” is stating an explanation.
When Sakurako said Takeru would get in the way (if he went to the club), this created a situation where Sakurako knows something Takeru doesn’t: the reason she says he would be a hindrance. In order to fill in this unknown, to give the reason why she said that, she says “It is that (Ayumu is in love).”
The explanatory の is one of those things that when it finally clicks, it becomes very clear.
Although you may have seen this already (as I linked to it in this thread earlier), I did a write-up on the explanatory の that I hope helps it click for some people.
I agree on this, that it’s adding a bit of emphasis to the statement.