How did people from different classes interact with one another in medieval europe?

Medieval society was rigidly hierarchical, with everyone expected to know their place. Most people believed that the division between the classes had been ordained by God; in a deeply religious age this was widely accepted as the natural order of things. To a large extent, the class into which you were born was the class in which you died. In the days of feudalism, peasants were pretty much tied to the land. They lived and worked on estates belonging to the nobility, to whom they were duty bound to give service. If you were a peasant in those days you couldn't just up sticks and seek better opportunities elsewhere; you owed your subsistence, your whole way of life to the lord of the manor and so you wouldn't be allowed to live anywhere else.
Although relations between the classes tended to be quite deferential, social disorder was still quite common in Medieval Europe. Peasant revolts took place with frightening regularity, often in the wake of a failed harvest. Desperate peasants would take out their anger and frustration on their alleged social superiors and their property—looting, destroying, in some cases even killing. Order was often quickly restored, but not before huge damage had been done.
Feudalism was largely destroyed, not by peasant revolts, but by the Black Death. This deadly plague wiped out around 60% of the population of Europe. It was no respecter of rank or wealth and many nobles died during this unprecedented catastrophe. With the ranks of the nobility decimated by the plague, society changed dramatically. A shortage of peasant labor meant that workers on the land could command higher wages and break free from the control of their lords and masters.
Medieval society, though still hierarchical, was now much more fluid. A wealthy middle-class quickly emerged, taking advantage of the economic opportunities inadvertently provided by the massive reduction in population. Though the population was much smaller, demand for basic goods remained high, and the rising middle-classes such as merchants and traders made huge fortunes from supplying them.

What is the theme of "The Moving Finger"?

The theme of "The Moving Finger" is generally regarded as relating to control. Ralph's first wife controls him so thoroughly that he is compared to the host for a parasite. He loses himself entirely; he isn't even aware of himself until she passes.
When Ralph marries the second Mrs. Grancy, he lives his fullest life through his happiness with her. If he is to be believed, the relationship was truly mutual, and they were both so overcome with joy at their union that their unexpected and sudden separation when she died was almost incomprehensible to Ralph Grancy. He realizes, through her continued "presence" in his life (it is not clear in the story if this presence was real or imagined), that he needs to bring her along, so to speak, into old age so that she will not be alone without him, even in death. This is why Ralph asks Claydon to age the masterpiece he painted of Mrs. Grancy—so that the couple can, in a way, grow old together.
Claydon believes himself to be in love with Mrs. Grancy, though the reader is given no clear indication that those feelings were ever returned. What both men share is a love for this woman that becomes obsession. Whether there is a paranormal occurrence that allows Mrs. Grancy to take hold of these men in the afterlife, or their fantasies grip them to the point of delusion, Mrs. Grancy has a firm hold on both men. Claydon uses his innate knowledge of Mrs. Grancy, and Ralph's desire to continue experiencing his life with her, to nudge him into death with merely a look upon the portrait's face. This is how Claydon comes to own Mrs. Grancy (the portrait) once and for all, remaking her back into his ideal image of her.
This control is nuanced; neither man is trying to control or manipulate Mrs. Grancy as she was when living. They have literally objectified her, projecting all their fantasies onto a portrait. Ralph Grancy idealizes unyielding companionship. Claydon idealizes the point in a woman's beauty when youth has ripened into womanhood, where innocence and experience exist in balance.
Both men want so badly to seize onto how Mrs. Grancy made them feel in those moments that they wanted her frozen at those moments in time—not because they desire to own the woman, but because they feel compelled to own those fleeting moments when they saw themselves idealized in her. They were chasing their own reflections in her face, like wanting to catch time in a jar.

One important clue to the story's theme is the title, "The Moving Finger." This is a quotation from a poem that was very familiar in Edith Wharton's day. Her story was published in 1885.
The phrase is part of one of the most well known passages of Edward Fitzgerald's 1859 translation (really, a liberal interpretation) into English of parts of The Rubáiyát of Omar Khayyam. Khayyam was an eleventh and twelfth century Persian astronomer, mathematician, and poet. His long poem was popular in artistic and intellectual circles in both England and the U.S.

The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it.

The idea is that fate or time moves with its own force and that no human action--whether based in faith or intellect or emotion--will have any effect on that.
The theme of these lines and the story is that we cannot change the past or the future.
Both Ralph Grancy and Claydon tried to alter reality, the former by asking that Mrs. Grancy's portrait be aged and the latter by doing the work. While the narrator is horrified at Claydon's actions, the artist is correct that his actions did not kill Glancy. The moving finger simply wrote its unchangeable story.
http://classics.mit.edu/Khayyam/rubaiyat.html

One of the themes of "The Moving Finger" by Edith Wharton is control—or, rather, the lack of it. However hard he tries, Ralph just can't seem to move on with his life. His sense of loss at the death of his second wife is ever present and haunts his every waking hour. Ralph is controlled by his past. As he cannot break free from the memory of the second Mrs. Grancy, Ralph tries desperately to exert some control of his own. There is a hint that perhaps Ralph's second wife had an affair with Claydon, the portrait painter. For Ralph, this must have represented a considerable loss of control over his life. One could argue, then, that in getting Claydon to repaint Mrs. Grancy's portrait to make her look older, Ralph is taking back some of the control he lost when his wife cheated on him.

How are Lia and Cassie connected?

Lia and Cassie are two of life's perennial outcasts. They're going through some major problems in their lives and as a consequence feel disconnected from the world around them. More than anything else, it's this overwhelming sense of isolation from a world they don't understand and which doesn't understand them that joins them together.
In addition, like a depressingly large number of girls their age, they both suffer from eating disorders; Lia is an anorexic, whereas Cassie has bulimia. For both girls, eating disorders are a way for them—one of the few ways available—to feel that they can exert some measure of control over their lives. But this is a mirage. To a large and damaging extent, Lia and Cassie's low self-image has been determined by society's expectations of what's considered the appropriate body-shape for girls of their age, and they've internalized those expectations, with truly disastrous consequences.

How, David realizes, do the people mistake his mercy for fear?

Absalom and Achitophel is a political allegory on events in Restoration England. The character of King David is meant to represent Charles II, who ruled England between 1660 and 1685. In Dryden's epic poem the Jews are presented, like late seventeenth-century Englishmen, as being stubborn and self-willed. As such, they are profoundly dissatisfied with David as their king, despite his mild, benevolent rule. They constantly plot against him, believing that they have the God-given right to overthrow a monarch who doesn't meet with their approval. Dryden is making a satirical point here, criticizing those of his contemporaries who took advantage of Charles's good nature and benevolence to undermine his rule.
One by one, the people David thought were his friends and allies start to desert him. The people are on the brink of revolt, convinced that David's mercy is a sign of weakness. Revolution's in the air and it seems like only a matter of time before the king is violently overthrown. Those remaining loyal to David such as Hushai and Adriel advise him that he must act firmly if he's to hang on to his throne. No more Mr. Nice Guy; David needs to assert his kingly authority and fast.
https://www.poetryfoundation.org/poems/44172/absalom-and-achitophel

In the article “Reality TV Gives Back: On the Civic Functions of Reality Entertainment” by Laurie Ouellette, how does the author use the rhetorical appeals of pathos, logos, and ethos to construct her argument that reality TV is actually beneficial to society?

In classical rhetoric, there are three primary forms of argument: pathos, ethos, and logos.
Pathos is an appeal to emotions. It focuses less on facts and figures and more on making the audience feel something.
Ethos is an appeal to character. It inspires the audience to act a certain way or points to the character, experience, or expertise (or lack thereof) of someone as an argument for or against something. An argument by ethos may quote the opinion of an expert to prove a point, for example.
Logos is an appeal to logic. It focuses on using reason and facts and figures to make an argument.
Oullette uses all three techniques to make her argument that reality television is beneficial to society. Here are some examples:
Pathos: Reality television encourages viewers to sympathize with the hardships and stories of the people on the show. It often uses emotional appeals to convince viewers to give or volunteer.
Ethos: Many reality shows focus on improving the character of those on the show. For example, Oullette points out that the show Secret Millionaire helps make wealthy citizens aware of the wealth imbalance between themselves and the poor.
Logos: Oullette believes that reality television has taken the place of documentaries as a way of "citizen-building". She states that reality television shows can be used to educate and promote positive behavior. She gives examples of reality TV being used to promote charitable activities or bring attention to the plights of others. Oullette argues that although the situations on reality television are often embellished and exaggerated, that does not negate the positive message they can convey.

Ethos--she builds ethos by referencing a variety of sources including starting with an opposing viewpoint. Throughout the essay she provides a variety of examples and quotes a large number of other sources. There is little doubt that she is well versed in the topic. Her academic tone and professional language also provide evidence that she is a trusted source.
Logos--If you look at current reality television within the context of the current political reality--post-welfare--of this essay, then you must accept that there is an inherently civic aspect to reality television.
Many reality television shows feature good civic behavior like volunteering and giving back. This models positive civic behavior and to a certain extent normalizes it which will have a positive impact on the viewers--monkey see; monkey do.
Pathos--There is a pride in American reality television as compared to the British reality television. "Do-good television is especially common on commercial channels in the United States. Although European public broadcasters offer reality-based lessons on living, most lack the resources to intervene directly in reality on a philanthropic scale." This pride will encourage the audience to respond positively to Ouellette's message. There is an American pride, and perhaps even a generational pride, in the do good message of more modern reality television shows which supports the idea that society benefits from them.

Who were the Britons, and what are the four nations of Britain?

The Britons (meaning those who live in Britain) were one of few native peoples inhabiting Britain before the Anglo-Saxon invasions of the fifth century; they were once believed to be descendants of the Celts. The four nations that comprise the modern-day United Kingdom of Great Britain and Northern Ireland are Wales, which was annexed by the Laws in Wales Act of 1542 by King Henry VIII; Scotland, following its union with Great Britain with the 1707 Acts of Union; Northern Ireland, after Ireland joined in union with the United Kingdom in 1801 and five-sixths of Ireland seceded in 1922, with Northern Ireland being the sixth piece to stay; and England. As of 1922, England, Wales, Scotland, and Northern Ireland are the four nations that comprise the United Kingdom.
https://learnenglish.britishcouncil.org/general-english/word-on-the-street/loch-ness/four-nations

What were some of the costs of the laissez-faire approach to economics for American workers?

While the premise behind laissez-faire economical philosophy driving much of American capitalism is that by minimizing and limiting the regulatory power of the government over the economic activity of the society, the "invisible hand" of market and capitalism will lift everyone up ("all are in one boat, thus all are lifted by the wave" concept) from their current socio-economic levels. The proponents of the laissez-faire economic philosophy also argue(d) that it will be in the necessary self-interest of everyone to ensure that everyone's rights are respected, otherwise, there are bound to be costs to the businesses in one way or the other.
However, in reality, this has not happened, as the American version of capitalism does not provide the framework to stop unfortunate individuals from falling so far to the bottom that they never can recover - compare the American approach to severe economic crises to say, the approach(es) employed in Germany, for example.
Another example is the perverse effects of laissez-faire economic system in America, especially in the healthcare industry - where an ever-growing share of the sector is devoted simply on the bureaucratic processing of the claims and counter-claims by myriad players and middleman in the healthcare system, thus depriving the patient (the customer!) of true transparency in the costs of medical procedures and medications.

According to the doctrine of laissez-faire, governments should intervene as little as possible in the running of the economy. They should simply set the rules and the legal framework in which businesses operate and stand back and allow market forces to work freely.
The downside of this approach, especially in late 19th and early 20th century America, was that workers went unprotected from the excesses of industrial capitalism. Without proper regulation or government control, businesses could get away with driving down or ignoring safety standards, leading to numerous work-related deaths and injuries. Workers could be routinely exploited by their employers, who could keep wages as low as possible—especially during a recession—safe in the knowledge that there were countless others willing to take their place.
Laissez-faire was consistent with a thoroughgoing hostility toward labor unions. The prevailing economic doctrine held that unions interfered with the operation of the free market in labor and that their activities should therefore be curtailed. With lack of protection from either the government or labor unions, workers often experienced shocking pay and conditions. This led to growing demands for change which, in due course, sounded the death knell for laissez-faire.