The host is described as "confrontational" in the sentence; the host is also mentioned as having critics. Those critics would be upset and angry with the host. Of all the choices, only "ire," meaning anger, has the appropriate meaning.

The last phrase of the sentence, "could never leave," is the key to finding the answer. The correct answer will essentially mean "never leave." "Perpetuity," meaning forever or eternity, is the correct answer choice.

The speech is defined as not being "generous and gracious." The correct answer, then, should mean an angry or even nasty speech, which is the definition of "rant."

The sentence finishes by talking about the girl's wit, and parallels her wit to the answer blank. The correct choice will mean sharpness or clerverness, which is the definition of "perspicacity."

The suspect is accused of plotting a serious crime. The answer, what was discovered, will indicate the level of deception involved in the crime. "Subterfuge," meaning a trick or deception, is the correct answer.

The Duke continues to look down on "lower classes," which is contrasted with the correct answer. The best choice will then mean a belief in equality, which is the definition of "egalitarianism."

The phrase "conducting wine tastings so long," indicates he considered himself some kind of expert, and the correct answer should reflect that. "Connoisseur," meaning someone with refined taste and judgement, is the best fit in the sentence.

The best clue words in this example are "grammarian" and "linguistic history." The latter makes "histories" unlikely, if only because of the repetition that this would impose. It is perhaps tempting to use "meanings," as a grammarian would pay heed to meanings in explication—just as he would pay heed to the declensions and inflections of words;  however, if we are considering linguistic history (even if flawed), we are above all concerned with etymology, which studies (or at least purports to study) the history of words and the meanings that can be gleaned from such history.

The key word is in the second sentence is "err." It might be tempting for that reason to consider "error" or "mistake," but we are provided a specific type of error, namely a grammatical one: "solecism" matches the intended meaning most closely.

The first sentence leaves our meaning so general that any of the terms might fit (though the case for "gusto" is particularly weak). The second sentence gives us a much better limiting factor, namely, the beauty of his form as a swordsman. In this case, we are more concerned with form than brute strength or anything similar; therefore, while perhaps "celerity" or "ability" might distantly apply, "finesse" captures the ballet-like beauty most directly.