The subject of the sentence would "follow the same policies" as the "former President."  This indicates he supports the "former President," or at the very least agrees strongly with the "former President." "Acolyte," meaning follower and devotee, is the best choice among the answers.

The fact the subject had "no plan of action" is the best clue to the correct answer. This means the missing word will indicate that the subject has "made decisions" by feel. "Caprices," meaning whimsies or fancies, is the best choice among the answers.

The subject had been "eating only nuts and berries," which is what colors his perspective on "the diner's limited menu."  The correct answer will reflect that the menu appeared to be full of options.  "Cornucopia," literally a horn filled with fruit, but used here symbolically, is the best answer choice.

A "compromise was never a likely outcome," because of the missing word being had by "both sides." The correct answer needs to indicate a hostility or opposition to deal making. "Intractability," meaning stubbornness or difficulty, is the best choice among the answers.

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."