The sentence compares the missing word with her original position as "an outsider." The correct answer will demonstrate a position of importance and primacy in her field.  "Luminary," meaning a leader and eminent person, is the best choice among the answers.

The sentence notes the plot is "tired," indicating the use of the "evil villain" is fairly sterotypical. The correct answer must indicate similarly hackneyed tropes. "Minions," meaning servants or underlings, and often indicating ineptness, is the best choice among the answers.

The "influential generals" are affecting the "weakened government."  This indicates that they have an outsized effect, and the correct answer will reflect this. "Coterie," meaning a small group or clique of like minded people, is the best answer choice.

The actual numbers at the protest, "a few hundred," stands in contrast to the group's claims of "thousands of protesters." This indicates the group was exaggerating for effect, the definition of "hyperbole."

The leading word Although lets you know there will follow a contradiction or logical conflict in this sentence. In this case, it is between the speaker's imagined skill at gambling, as evidenced by the phrase "I felt confident that my mathematical abilities would give me a leading edge in Vegas," and the word you aim to find. You should be on the lookout, then, for a word that inverts "having the leading edge," keeping in mind that the speaker specifies this is their first time gambling. "Tyro" means novice, or extremely inexperienced person, so it is the best fit here.

Notice that the word "tin" is in quotes. The clause "the foil being made of aluminum rather than tin" tells you why: since tin foil isn't actually made of tin, its name does not make much sense. This lets you know that the word you are looking for means a nonsensical or mistaken name; the only choice that fits the bill is "misnomer."

You are told that the wealthy man has something against donating to charity and that his countrymen see this as "evidence of his stingy and selfish nature." You can tell by the fact that he staunchly turns down every plea that the man must be consistently, stubbornly opposed to charitable donation; therefore, you should look for a word that means "stubbornness."  The word "intransigence" means stubborn or immovable, and is the best choice for this question.

"Cynicism" is the belief that people are motivated by selfishness. 

"Alacrity" means enthusiam or eager willingness.

The key phrase in the sentence is that the subject "never went to church," indicating he is not very religious.  This can rule out "zealot," "reformer," and "iconoclast," which, in the context of religion, all indicate an engagement with religion on some level. "Libertarian" can be ruled out as it describes a political position.  "Atheist," meaning someone who does not believe in God, is the correct answer.