To “ruminate” on something is to return and ponder over it through the day.  The only other option that might seem plausible in this regard would be “brood,” but that has the added negative connotation of thinking about something unhappy.  The word “ruminate” originally comes from Latin roots meaning to “chew over.”  It is used to describe animals like cows, which are named “ruminants.”  Such animals chew the food that they regurgitate from their first stomach (their “rumen”). 

There is no indication in this sentence that John and his friends are in the midst of debating his charm (or lack there of).  Therefore, the word “fancied” is the best choice, as it means “to think or imagine.”  The word is derived from the older term “phantasy,” meaning “imagination.”  This term itself was derived from the older philosophical terms “phantasia” and “phantasm,” which were parts of the theories of knowledge particularly found in medieval scholasticism but likewise stretching all the way back to Aristotle.

When arguing, one sometimes has to assume some fact or other in order to make an initial argument.  To “posit” something is to “place” such a fact forward as a possible explanation.  Generally speaking, such things are assumed to be true, though they are used as an investigation tool to start an argument that would otherwise be impossible without some initial test assumptions.  Insofar as the word means “to place,” you can see that it is related to English words like “position,” “impose,” “postpone,” and “reposition.”

Although a number of these options are tempting, the clear sense that the sentence wishes to convey is that Patrick wishes to lead his friends and neighbors into seditious activities.  When someone tries to encourage others to undertake such illegal acts (even if justified) is said to “incite” these others.  Although the term might be used merely to mean “to stir up,” it generally has this negative connotation.  Insofar as it is related to such “stirring up,” the word is related to the word “excite.”

According to this sentence, Paula is in need of funds that can be spent immediately, something that cannot be done by well with real estate, an asset that has worth but must be sold before it can yield its value.  “Liquidation” occurs often when one is selling assets in order to settle debts.  However, one can also be said to “liquidate” assets into a cash form that can be spent readily. 

When one channels something, he or she redirects it from one location to another.  Vincent is clearly doing this, having resolved to transfer is energy from his annoyances to productive work.   The word literally indicates a structure (manmade or natural) that allows fluid to flow, though it is often applied to any sort of medium (even electromagnetic) allowing for the passage of content from one point to another.  It is related to the word canal.

In this sentence, there is no implication that Timothy’s girlfriend would be nasty in trying to convince him into changing his attitude. The only thing that is indicated is that she is “indefatigable,” a word meaning “untiring;” therefore, the best option would be “cajole,” which means to persuade insistently or even through flattery. Though no flattery is implied in our sentence, the insistence is implied, and that suffices in comparison with the other options.

Since the child is stealing something insignificant, the best option is “pilfer.” Although several of the options pertain to stealing, only “pilfer” adds the sense of taking something of little value—in this case, “some small candy.”

When someone “goes beyond” the boundaries, he or she is said to “transgress” them. The “trans-” prefix means “across” as is evident in words like “translate” (to carry across—languages in this case) and “transform” (to change “across” from one form or appearance to another). The “-gress” comes from the Latin for “to walk or step” found in English words like “gradient,” “grade,” and “egress.”

When someone “niggles” over the details of something, he or she criticizes minor details. In our sentence, this best captures the sense hinted at by the sister’s “streams of critical remarks over the minor details . . .” The verb “to niggle” can also be applied to one who is “niggling” over the details of a given work, even his or her own. Someone who never is satisfied with the small details of his or her (e.g.) writing will often “niggle” over these details incessantly.