Here, Peter’s character is contrasted with the taciturnity appreciated by his friends. When one is taciturn, he or she uses words sparingly. Therefore, the best contrasting word would be “prolixity,” a word meaning that one speaks too many words. It is derived from the prefix “pro-” for “forward or outward” and “-lixity” from the same root from which we get “liquid.” Therefore someone who is prolix is one whose words can be said to “pour forth” like too much water.

If someone is the opposite of being understated, he or she would draw too much attention to himself or herself. When one is “ostentatious,” he or she displays things in a gaudy manner, particularly in order to draw attention to himself or herself and be noticed.

The implication here is that the work of astrophysicists has been more capable and effective in bringing forth practical advances (in comparison with theoretical mathematicians). When one can bring forth results in an effective manner, such a person (or institution) is unsurprisingly called “efficacious.” This word has many relatives, as might be surmised, such as “efficient,” “effect,” and “efficacy.”

This sentence works by way of contrast, as you can tell from the word "although" in the second clause. The description in that introductory clause is implied with regard to the wealthy people mentioned in the first clause. If someone does not give even a penny of money, he or she gathers all of his money for him- or herself. While perhaps the money is invested, the general sense of the sentence is merely to point out such acts of gathering and keeping money. To "hoard" things is to do just that. The word can also be used to describe the things that have been gathered together and amassed in this fashion.

The second clause furnishes the clues that we need. It implies that without the ability to cope with changes, a healthy psyche is likely impossible. This means that you must have this skill—it is not optional. Such things are "essential." In much older philosophical language, "essential" things were contrasted with "accidental" ones. The latter were not "accidents" in the sense that we generally use that word; they were things that just happened to come along with something. For instance, it is essential to a person that he or she be able to think (or at least potentially be able to do so). It is wholly accidental if he or she has black or blond hair. In this sentence, it is said that it is a necessary and essential aspect of psychological health to have the ability to cope with changes.

The best clue for this sentence is the expression "that was soon to assault them." This implies that there is going to be an even stronger storm soon. The option "trickle" might seem like a good way to characterize the weaker first storm, but that really does not fit the sentence—neither in style nor really in grammar. A "prelude," however, is something that introduces another thing, generally being less important than that later thing. For instance, a "prelude" before a musical show lets the audience here some of the music but does not really give them the whole show at once. That comes later. The word literally means to play before. In the sentence, the first storm is said to be a mere prelude to the one that is soon to come.

Yes indeed, the heart is "cardiac"—the only "cardiac" (associated with the heart) organ in the body. This is not very informative. The same goes for "internal." The sentence clearly wants to set up an opposition between the gallbladder and the heart. You can tell this by the use of the word "although." The gallbladder is not absolutely necessary—you can live without it. The implication is that the heart is necessary. Something is "vital" when it has such necessity, particularly for living. (The word comes from Latin roots related to "life.")

Often, the best approach to a sentence is to try to "fill in the blank" yourself. For this question, consider the fact that the two halves are contrasted. The gadget appeared to be one, single machine. In fact, it actually was "made up" of a number of interrelated ones. The idea is that it was a group of machines, gathered together and interrelated. When you compound things, you mix together (and generally connect) various elements. To "confound" is to cause confusion—don't be confused by this expression of confusion! The other options are likewise quite inappropriate for the purposes of this sentence.

The contrast here is between the types of style under discussion. In the introductory clause, we are discussing Flavia’s ability to write "verse"—poetry. The passage implies that she also had an excellent “non-poetic” style. Prose writing is non-metered writing, and this is the best contrast to “metered verse.” “Writing” is too general, “didactic” means for teaching purposes, and even “essay” does not contrast to “meter” as directly as the word “prose" does.

The contrast in this sentence is between the “simpler and poorer” conditions of the brothers’ childhood and that of Gilbert’s brother today. Indigence and destitution are extreme poverty, so these options are not at all opposite. While stereotypes might tempt us to think of the rich as being "arrogant," we must not go beyond the direct meaning of the sentence. “Posh” describes a luxurious manner of living, and this well contrasts with the brothers’ upbringing.