The <span>word in the sentence does the adjective clause modify is letter (</span>C.) babysitter. Adjective clause functions identically with adjectives that uses the indicators such as the pronouns who, whom, which, and that; or the adverbs where, when, and why.
I would say <span>b. The band played songs for the crowd with guitars. it sounds very awkward because "with guitars" should be placed after " the band played songs" and a comma placed after "the band played songs".
so this is what it should look like
The band played songs, with guitars, for the crowd
Hope it helps!
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It is somehow related because Sad Perfect is a book about a girl who has an eating disorder, as you know this is not an easy thing to deal with so it would not be uncommon to hate your life. It's not a quote from the book but it can relate.