Since the politician’s fortunes had changed so greatly, it is fair to say that he has gone from being “on the top of the world” to being on the “lowest rung.” When one is at his or her “nadir,” he or she is at the lowest point of his or her fortunes or accomplishments. Do not be tempted to think that the best option would be “ruination” or “unraveling,” for while these may indeed be true, the focus of the sentence is clearly on the fact that this is a low point in comparison with the rest of his career.

The key thing to note here is that the appointee is being assigned to a colonial office and that said person will be acting as a representative, not as a replacement. Such a person is called a “viceroy.” The prefix “vice” means “in the place of,” as one sees in the case of “vice president.” The ending “roy” is related to the French for king, “roi,” which ultimately is related to other words from the common Latin base meaning king or ruler, as founding words like “regal,” “reign,” and “interregnum.”

The pivotal clues for this sentence are “initial evidence” and “potential research project.” This implies that the person has not yet started the project. While perhaps he or she could be presenting "opinions," the general implication is that he or she is undertaking some new research. When we start projects of this sort, we often lay out a thesis or hypothesis, upon which we will further elaborate with the passage of time.

The wall stands between two areas, functioning as the means by which sound passes between rooms. Though some medieval men had intriguing reasons for misunderstanding this phenomenon, we know better now. The word “medium” means middle or between. It can be used as a noun meaning the substance traversed by something like light, electricity, or (indeed) sound.

The key thing to note is that the butler serves in such a way as to often overlook his own desires. This does not necessarily imply love or even uprightness, but it does imply that he is unwavering in his service. Such a spirit is one of “dedication.” The word comes from the Latin base for the word for “consecrating” and is also somewhat related to words like “dictation,” “diction,” and so forth.

The key thing to note here is that Mark is a “deserter” from having been a faithful citizen.  Although perhaps he is a troublemaker and even a misfit, the word “renegade” best expresses the idea of deserting that to which one once was devoted. In this word the “re-” prefix does not mean “again” but instead merely strengthens the main portion of the word—the “-negade” portion of the word. This portion comes from the same roots as “negative” and “deny.” Here, the sense is to deny forcefully one’s former attachment.

This problem is an example of one for which you have to find the “least bad” answer. The descriptor that we are looking for regarding kings is one that is opposed to being democratic. (This is indicated by the expression “that they would act in such an undemocratic manner”). Many of the negative terms could apply, but they go further than this implication. The word “potentate” can mean merely a monarchical ruler, but its broader implication is that such a ruler acts solely by his or her own power, without any consultation of others. The word itself is derived from Latin roots for “power,” found in many English words like “potential,” “possible,” “omnipotent,” and “impotent.”

Although the minister might be giving a sermon or even an oration to the congregation, the sentence most directly indicates that whatever he is doing involves “giving prase and thanksgiving.” A “doxology” is a formulaic prayer giving thanksgiving to God.  It comes from the combination of the Greek words for praise (“doxos”) and word (“logos”). The latter is used in many English words pertaining to subjects of study (such as “biology,” “logic,” etc.).

When one departs from accepted norms, he or she might be called many things, but it is most appropriate here to call such a person a “maverick.” The term comes from the surname of Samuel A. Maverick, who did not bother to brand his cattle. Such unmarked steers thus became known as “mavericks” since they didn’t fit into the standard system of animal control. 

The sense of the blank is that Martin lacks drive and energy to undertake his tasks.  “Lassitude” expresses such a state of weariness.