The clause that needs filling-in is simply a rephrasing of the first part of the setence—"stressed" is the closest synonym of anxious and therefore makes the most sense in the sentence.

The subject of the sentence knows that he is going to cause someone displeasure, therefore he is being mischeivous—"devilish," when used in this context, means the same thing; therefore "devilishly" is the correct answer.

We can infer that because Fred "shouted at the first person to ask him about [the math quiz he failed]," we need to pick out an adjective to describe Fred that means something like "irritable." "Charismatic" might look like a potentially correct answer, but "charismatic" is an adjective that means "exercising a compelling charm that inspires devotion in others," so it wouldn't make sense in the sentence's context. "Touchy," however, is an adjective that means "oversensitive and irritable" when being used to refer to a person, and because "touchy" best describes Fred's irritable mood, "touchy" is the correct answer.

We can infer that because the period of sunny weather lasted "only ten minutes," we need to pick out an adjective to describe the sunny weather that means something like "fleeting" or "temporary." "Lasting," then, cannot be the correct answer, because "lasting," when used as an adjective, means "enduring or able to endure over a long period of time," making it an antonym of the word for which we're looking. "Evanescent," however, is an adjective that means "soon passing out of sight, memory, or existence; quickly fading or disappearing," and because "evanescent" best conveys the briefness of the sunny weather in the sentence, "evanescent" is the correct answer.

The answer that makes the most sense is "debilitated," to weaken or enfeeble.

"Eloquent" means having a skillful way with words or speech. "Mundane" means ordinary or day-to-day. "Placid" means calm or mild. "Symbiotic" means interdependent, coordianted, or unified. "Taciturn" means quiet, mild, or reserved.

"Cantankerous" means crabby or irritable. "Avuncular" means consultive or helpful. "Bucolic" means rustic or rural in nature. "Complacent" means calm, confident, or pleased. "Jocular" means funny or cheerful.

"Lucid" means comprehensible, clear, or understandable. "Wary" means careful or cautious. "Peripheral" means minor, outside, or incidental. "Nebulous" means murky, confused, or obscured. "Insolent" means bold or disrespectful. 

While the adventurer's mosquito net might very well be "impeccable" (flawless), "acrid" (smelly) or "elongated" (if he was perhaps a very tall adventurer), all that we know for sure is that light can shine through it—and that is the exact meaning of "diaphanous."

"Obdurate" means pigheaded or stubborn. "Antediluvian" means out-of-date or prehistoric (ante=before, diluvian=the flood). "Bucolic" means rural or rustic in nature. "Didactic" means educational or explanatory. "Palpable" means clear or obvious.