The sentence that has faulty parallel structure is option B. To make it parallel should be to parents, to teacher and to students
Faulty parallelism is a construction in which two or more parts of a sentence are equivalent in meaning but not grammatically similar in form. Option B does not follow the same grammatical pattern
I love to write papers. I would write one everyday if I had the time.
Or in one sentence:
I love to write papers and I would write one everyday if I had the time.
For the first part- luscious seems to fit the gracious description of the pastries.
And for the second question I'd say 'Gentle or friendly criticism or advice.'
Admonition is to advise or warn someone.
A key word from the passage to support my answer would be the word 'nudging' because when you think of the action of nudging it is a gentle motion of contacting with something.