This sentence hints at the use of an intensification by means of the word "mere." The investigator's work was no "mere examination." That is, it was not some minor affair, looking into the superficial details. Instead, the work was veritably (that is, "truly"—like words like "veracity" and "veracious") a deep inquiry into matters. An "inquisition" is just such an investigation. We often think of this word in connection with the Spanish Inquisition, but it means, more generally, a profound and detailed inquiry. For the first blank, we merely need a word that works well to express what was the subject of the inquisition—i.e. the facts of the case!

People who are "scrupulous" are fussy about details, paying extreme attention to them. The options "heed," "notice," and "attention" (and perhaps even "deference") all are potential options for the first blank; however, the general idea of the sentence is that scrupulous people do not merely pay such attention to the law. They have a strict adherence to it. (This is what is meant by having "stringency.") When someone is legalistic, he or she adheres to every detail of the law without bending. Hence, the best combination is "heed . . . legalism."

A "braggart" is someone who is boastful and arrogant. "Aggrandize" means to exaggerate. These words contrast with the idea of the man being charming. "Although" is a key word to look at. With that word in place we know we are looking for an opposing sentiment to the first part of the sentence. 

"Acuity" can be defined as mental sharpness or understanding, "query" as a question. All of the other definitions don't fit the context of the sentence.

"Egotism" means selfishness; "affront" means insult.

"Voracity refers to greediness; "quailing" refers to trembling.

"Pugnaciousness" means determined aggression; "resistance" means struggle.

"Obsequiousness means prone to excessive flattery; to "protest" is to dissent.

The sentence clearly indicates an intensification. This is hinted at by the word "merely" and the construction that follows it in the second independent clause. To solve this question, begin with the second blank, which is more obvious. If the parents want their children to fulfill their potential, the best option is "flourish." This describes how someone's potential could come to full flowering, as indicated by the clues in the sentence. The sentence is not about elation or triumph, so do not be tricked by those options.

Regarding the first blank, it is very easy to find a word once you have determined that "flourish" is the best option for the second blank. The parents in question do not want their children merely to "do well enough." That is, they do not want them merely to survive. 

The general idea of this sentence is that Paula had undertaken many "other-centered" actions for her family. This apparently led her to really dislike these sorts of activities. We can tell that she didn't like them much by noting the expression "for others in any way whatsoever." This hints at a very strong dislike. Actions that are "other-centered" or "other-focused" are altruistic actions. For the second blank, only "abhor" really captures the idea of really hating to do such things.

Clearly, Lisa only wants to refer to the hairline in an indirect manner (at best). Since the hairline is receding, it is "going back" across his head. (This is, of course, the meaning of "receding.") The verb "ebbed" means "to go back or out."  Often, we talk about the tides ebbing back out to sea. We could apply this idea to the hairline, even if it is not a normal manner of speaking. The word "obliquely" means indirectly. This is indeed how Lisa wants to approach this manner, given her fear of insulting the man.