What is a significant quote from chapter 2 of Animal Farm?

Animal Farm has its beginnings in chapter 2 as the animals rename "Manor Farm" as "Animal Farm" having planned and executed the rebellion and driven Jones from the farm. The principles of Animalism are etched on the barn wall.

The Commandments which include the mantra of four legs and the fact that two legs signifies the enemy culminate in

"7. All animals are equal."

It is significant that this is the last and seemingly most important commandment: yet, already the basis of equality is questionable as the animals, looking forward to a share of the milk, are denied it. Later, they will discover that the needs of the pigs, the "brain workers" necessitate (apparently) such unfairness.   

Even at the early stage, the naivete of the animals lends itself to abuse of power as they will not question their oppressors. Boxer is a prime example:

"Napoleon is always right."

The animals' inability to recognize the pigs' motives is significant because it condemns them to a life of hardship and manipulation at the hands of corrupt leaders.

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What motto does Old Major give the animals in Animal Farm?

What is interesting is that all this works out quite differently in the end.  In the final chapter, the term "comrade" as a way for the animals to address each other is forbidden, and the "pigs" have taken on all the characteristics of the "men" who were enemies.  So the animals final state may be worse than their first.  They have new leaders who could care less about them, and they have been forbidden to be comrades to each other.  History may be a circle, but in their case it seems to be a descending spiral.

'All men are enemies. All animals are comrades.'

The simplistic attitude of Old Major shows that the concept of communism is indeed difficult to put into practice, as the farm animals will soon learn:

"...we are deluding ourselves if we think we are closer to those revolutionary ideas of justice, brotherhood, and equality than were the citizens of Stalinist Russia."

"...such descent from idealism to totalitarianism is inevitable in any violent revolution."

 - from 'Historical Setting for Orwell's Animal Farm'

   in enotes' 'Animal Farm Essays and Criticism'

At the beginning of the novella, old Major gives a moving, passionate speech, where he encourages the animals to rebel against their human masters and establish an egalitarian society ruled by animals. Old Major focuses his speech on the oppressive, malevolent nature of humans and labels human beings as an animal's worst enemy. Old Major elaborates on the various ways humans oppress animals on the farm and encourages them to rise up against their masters. Old Major's motto is

Whatever goes upon two legs is an enemy. Whatever goes upon four legs, or has wings, is a friend (Orwell, 5).

He then proceeds to warn the animals about adopting human habits and behaviors. The intelligent pigs eventually adopt Old Major's warnings and use them to create the Seven Commandments. Following the death of old Major and the creation of the Seven Commandments, old Major's motto is then reduced to a single maxim, "Four legs good, two legs bad," which is repeated on a constant basis by the unintelligent sheep.

What are some notable quotes from Snowball in Animal Farm?

At the beginning of the story, Orwell directly characterizes Snowball by writing,

"Snowball was a more vivacious pig than Napoleon, quicker in speech and more inventive, but was not considered to have the same depth of character" (7).

Snowball is utterly dedicated to the cause and risks his life during the Battle of Cowshed. Snowball not only plans the attack against Jones and his men but willingly puts himself into harm's way by charging directly at Jones. Orwell writes,

"Snowball now gave the signal for the charge. He himself dashed straight for Jones. Jones saw him coming, raised his gun and fired. The pellets scored bloody streaks along Snowball's back, and a sheep dropped dead. Without halting for an instant, Snowball flung his fifteen stone against Jones's legs" (17).

Snowball is also a motivating leader throughout the novella Animal Farm. He continually encourages the animals to work together to attain goals and promotes the tenets of Animalism. On the first day of the harvest without Mr. Jones, Snowball offers a challenge to the animals on the farm. Snowball motivates them by saying,

"Now, comrades...to the hayfield! Let us make it a point of honour to get in the harvest more quickly than Jones and his men could do" (Orwell 11).

Snowball is also a very intelligent pig who has the animals' best interests in mind. He works day and night developing plans to build a windmill that will make the animals' lives easier. Snowball captures everyone's attention whenever he tells them about his plans for the windmill. The animals are captivated by Snowball's speeches, and Orwell writes,

"After surveying the ground, Snowball declared that this was just the place for a windmill, which could be made to operate a dynamo and supply the farm with electrical power...The animals had never heard of anything of this kind before (for the farm was an old-fashioned one and had only the most primitive machinery), and they listened in astonishment while Snowball conjured up pictures of fantastic machines which would do their work for them while they grazed at their ease in the fields or improved their minds with reading and conversation" (21).

What is the most important passage in Animal Farm, pages 1–83, and why?

This question requires more of a judgment call than a clear right-or-wrong answer.

Orwell's Animal Farm would contain a multitude of important passages, and in many respects, the cumulative impact of these various passages in how they relate to and build off one another would be even greater than the impact of any single passage taken in isolation.

With that in mind, selecting one passage in particular would be largely based on your own personal opinion, and the key to this question is how you defend that choice, analyzing that passage as to why it is important and how it relates to the rest of the book. You can expect different readers to select different passages, and as long as they are all able to defend their selections with argumentation and analysis, their answers would be correct.

In any case, speaking from the early chapters of the book, two passages immediately come to mind as significant within the larger thematic structure of the book. The first passage is the initial statement of Animalism's Seven Commandments, found near the end of chapter 2. As you see throughout the book, the pigs will systematically rewrite and alter those original commandments to advance their own privileges and interests (essentially rewriting history). Thus, this initial passage is all the more important, for it presents these commandments in their original form before they are corrupted.

The second passage can be found in the three paragraphs that close chapter 3 (beginning with the sentence "The mystery of where the milk went to was soon cleared up"). This represents the first real expression of the pigs' corruption, as they begin to claim special status and privileges for themselves; but it is all the more thematically relevant for just how early within the narrative this can be found and what this means for Orwell's allegory. Note in particular that even Snowball is implicated in this corruption, agreeing with the other pigs and benefiting from their special status. What this suggests is that the corruption was already present from the very early stages, long before Napoleon set up his totalitarian regime.

These are only two examples, both from the early part of the book. Reading through the book, you can certainly find other passages of critical importance. The key will be analyzing why they are important and using that to advance an argument as to why one, in particular, is more important than any other.

What are some impactful passages in Animal Farm?

One of the most important and impactful passages in Animal Farm comes right at the end of the book:

The creatures outside looked from pig to man, and from man to pig, and it was impossible to say which was which.

These lines, the very last lines of Animal Farm, sum up in a nutshell what has happened to the Animalist revolution. The revolution started with high hopes, motivated by a passionate belief that animals could run the farm themselves without any human assistance. This was a revolution of dignity in which animals would be in charge of their own destiny and no longer have to suffer exploitation at the hands of humans like Mr. Jones.

But before long, the revolution ran into trouble, and Napoleon and the other pigs, backed up by the sharp teeth of the farm dogs, established a brutal dictatorship characterized by murder, famine, intimidation, and constant lies.

The animals were supposed to have been liberated by the Animalist revolution, but instead, they've been enslaved by it. Napoleon and the other pigs are little better than humans; in fact, they're even worse. No wonder, then, that when looking from one to the other, it becomes impossible to tell which is which.

What are some significant quotes from Animal Farm that connect to its themes?

I think that you are going to find lines or quotes from the work that will demonstrate the themes of how political power is something that is constantly fluid.  It is an entity that is coveted by those in the position of control.  Napoleon certainly demonstrates this as he ascends to power and seeks to consolidate it:

The animals would still assemble on Sunday mornings to salute the flag, sing “Beast of England,” and receive their orders for the week; but there would be no more debates.

From chapter 5, this quote helps to bring out how Napoleon recognized at an early moment in his control of power that the principles of the revolution, the same spirit that helped elevate him to power, could not be the same realities that he could use to help keep him in power.  Such a quote connects to Orwell's theme of how politics and political rule are often constructs of the individual who seeks to maintain and advance their own political control.