"Enmity" means hatred and hostility, while "seethe" means to be in a state of turmoil or anger but not show it overtly.  Two men who hate one another would, of course, find themselves in an agitated and angry state upon the sight of one another.

The words “mini-riot” and “exasperation” and the phrase “scene of crumpled papers and screaming children” indicate that the classroom fell into the lesser state of disorganization. Only "disarray" (a state of disorganization) and "deteriorated" (falling into a lesser state) meet these definitions.

To "belabor" means to go on in excessive detail about something. A "rant" is a long speech about something in a passionate way.

"Coalesced" means merged into a whole, while a "colossus" is a gigantic statue or thing. A football team's offensive line merging into one unit would certainly move like a gigantic thing, a colossus.

"Monotony . . . bores" is the only pairing that makes logical sense since “monotony” means tedious sameness and “bores” means to causes one to lose interest in something. Although "tedium . . . agitates" looks like an appealing choice, “agitates” actually means excites, the exact opposite of the meaning needed in the second blank.

The correct answer will refer to the musician's skill on the piano ("virtuosity") and as a result, how he is able to combine ("juxtapose") three different melodies in his performance. The incorrect answers either dismiss the musician's skill ("ineptitude" and "unfamiliarity") or do not use a verb that indicates that the musician combined the melodies ("transmute" and "promulgate").

The second sentence indicates that the bishop wishes to stop the movement.  It does not indicate any desire to persecute.  The word “arrest” might seem, at first glance, to carry the same negative, “persecuting” sense as some of the other options, but the word likewise can mean “to stop” as in the usage “arrested development” to describe someone who is stunted with regard to some kind of growth.  A “sect” is group differentiated by their beliefs, often with a negative connotation in regard to an accepted orthodoxy.

A "litigant" is someone involved in a lawsuit, while to "manifest" means, in this instance, to show plainly. Arguably, a sweating and presumably nervous litigant would reveal himself to be guilty.

The sense of the sentence communicates that Othmar’s fame is increasing. When something “waxes,” it is increasing in size or intensity. The word is normally used to describe the increasing of lunar light as the moon becomes larger (at least in its visibility, that is). This primary usage is often transferred in order to describe the growing of things other than the moon. The opposite term (i.e. the term for decreasing lunar light exposure) is “wane.”

The second word, “renown,” means fame, particularly in the sense of being discussed by many people. It is derived from roots related to words like “nominate” and “nominal”—words that have to deal with the notion of names (the “nom-” root).

As one ages (and becomes tired), they can be said to be in a state of “dotage,” meaning that they are old and weak. To step down from rule is to “abdicate” from it.