Is fear the underlying cause of conflict in The Left Hand of Darkness?

Fear is a major factor in many of the conflicts in the novel, but I don’t think it’s the sole cause of conflict. Fear predominates the first part of the story, when Genly is in Karhide. Genly’s mission is to bring the people of the planet Gethen to join the Ekumen, a loose federation of human worlds. To do this he must convince Gethen’s two distinct societies to agree to the union. The first one he approaches, Karhide, does seem to refuse the prospect out of fear. They distrust the unknown and are resistant to change. While in Karhide, Genly also shows fear himself in his relationship with Estraven. Estraven is genderless and formal, and he communicates in a style that is utterly unfamiliar to Genly; this causes distrust and suspicion.

But when he goes to Orgoreyn, one could argue that it is Genly’s lack of fear that gets him in trouble. The people in Orgoreyn communicate in ways that feel more familiar to Genly than the ways of Karhide. This familiarity makes him feel safe, despite Estraven’s warnings, and Genly is less cautious than he should be. His lack of fear leads to his arrest and subsequent condemnation to a work camp where he probably would have died if Estraven hadn’t rescued him.

I would say that the main source of conflict in The Left Hand of Darkness is assumptions. Genly often gets into trouble by relying on what he already knows instead of being open to not knowing. As he says himself, “Don’t you see how useless it is to know the answer to the wrong question?”

Is "The Yellow Wallpaper" crime fiction? If yes, what was the crime?

"The Yellow Wallpaper" by Charlotte Perkins Gilman is not an example of crime fiction or a crime story.
First, one should note that crime fiction is a genre defined by far more than the simple occurrence of a crime. Although crimes occur in many novels and plays, including Crime and Punishment, Oedipus Rex, and Hamlet, these are not considered crime stories because the main focus of the stories is not on the crime itself or its solution, but on the characters and society being portrayed, whereas in crime fiction, such as the stories about Sherlock Holmes, the focus is purely on the crime and its solution. Also, crime fiction is by its nature plot-driven. "The Yellow Wallpaper" is a character-driven story focusing on the mental deterioration of the protagonist, not action.
Next, there is no evidence of a crime. While the rest cure imposed on the protagonist is barbaric by our standards of mental health care, it was actually quite expensive (somewhat of a sacrifice for the family) and considered humane in its period. The protagonist's imagining a woman trapped behind the wallpaper is a hallucination that also serves as a metaphor for the protagonist's own state of mind, not some actual Gothic horror. 

What is the talk like between Ben Winthrop and Mr. Macy in Silas Marner?

It looks like you may be referring to the conversation at the Rainbow in chapter 6. That is the only evident instance when both Mr. Macey and Ben Winthrop participate in a conversation. Yet, Ben Winthrop and Mr. Macey do not directly address each other in this group conversation at the Rainbow.
Rather, they team up to tease Mr. Tookey by throwing out individual insults at the poor deputy clerk. During the conversation, Ben Winthrop (a wheelwright and the leader of the church choir) draws attention to Mr. Tookey's inability to carry a tune.
For his part, Mr. Tookey is insulted and demands proof of his supposedly inferior singing abilities. He asserts that there is always bound to be two opinions about something.
At this point, Mr. Macey makes a patronizing comment. He tells Mr. Tookey that he is indeed right and that "There'd be two 'pinions about a cracked bell, if the bell could hear itself." Mr. Macey's comment is rather insulting because it suggests that Mr. Tookey is like a "cracked bell" who can't hear how bad his singing is.
Of course, Mr. Macey's comment causes everyone to laugh at Mr. Tookey. Upset at being ridiculed, Mr. Tookey argues that it was Mr. Crackenthorpe who asked him to fill the position of parish clerk and that this position comes with the right to sing in the choir. At this, Ben Winthrop continues the refrain about Mr. Tookey's poor singing abilities:

"Ah! but the old gentleman and you are two folks," said Ben Winthrop. "The old gentleman's got a gift. Why, the Squire used to invite him to take a glass, only to hear him sing the "Red Rovier"; didn't he, Mr. Macey? It's a nat'ral gift. There's my little lad Aaron, he's got a gift—he can sing a tune off straight, like a throstle. But as for you, Master Tookey, you'd better stick to your "Amens": your voice is well enough when you keep it up in your nose. It's your inside as isn't right made for music: it's no better nor a hollow stalk."

Ben Winthrop's insulting comment leads everyone to conclude that he has bested Mr. Macey's "epigram" earlier about Mr. Tookey being a "cracked bell." So, the talk between Mr. Macey and Ben Winthrop can be said to be conspiratorial and sarcastic in nature. Both men team up to insult the harassed Mr. Tookey.

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 46

Determine $\displaystyle \frac{dy}{du}, \frac{du}{dx}$ and $\displaystyle \frac{dy}{dx}$ if $\displaystyle y = \frac{15}{u^3}$ and $u = 2x + 1$.

We first find $\displaystyle \frac{dy}{du}$ and $\displaystyle \frac{du}{dx}$.


$
\begin{equation}
\begin{aligned}

\frac{dy}{du} =& \frac{\displaystyle u^3 \cdot \frac{d}{du} (15) - 15 \cdot \frac{d}{du} (u^3)}{(u^3)^2} \qquad \text{ and } &&& \frac{du}{dx} =& 2 \frac{d}{dx} (x) + \frac{d}{dx} 1
\\
\\
=& \frac{-15 (3u^2)}{u^6} &&& =& 2
\\
\\
=& \frac{-45}{u^4} &&

\end{aligned}
\end{equation}
$


Then,


$
\begin{equation}
\begin{aligned}

\frac{dy}{dx} =& \frac{dy}{du} \cdot \frac{du}{dx}
\\
\\
=& \frac{-45}{u^4} \cdot 2
\\
\\
=& \frac{-90}{(2x+1)^4}
\qquad \text{Substitute $2x+1$ for $u$}

\end{aligned}
\end{equation}
$

Beginning Algebra With Applications, Chapter 6, Test, Section Test, Problem 22

Solve by addition method:
$
\begin{equation}
\begin{aligned}

9x-2y =& 17 \\
5x+3y =& -7

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

3(9x-2y) =& (17)3
&& \text{Eliminate $y$: Multiply each side of equation 1 by 3 }
\\
2 (5x+3y) =& (-7)2
&& \text{and Multiply each side of equation 2 by 2}
\\
\\
27x - 6y =& 51
&&
\\
10x + 6y =& -14
&&
\\
\hline
\\
37x =& 37
&& \text{Add the equations}
\\
x =& 1
&& \text{Solve for } x

\end{aligned}
\end{equation}
$


Substitute the value of $x$ in equation 1


$
\begin{equation}
\begin{aligned}

9(1)-2y =& 17
\qquad \text{Solve for } y
\\
9-2y =& 17
\\
-2y =& 8
\\
y =& -4

\end{aligned}
\end{equation}
$


The solution is $(1,-4)$.

How do both the poem and the story itself compare with nature?

I remember the first time reading this story.  I thought it was so cool.  I didn't quite understand the poem, and I definitely didn't understand the poem as it compared with the story.  Then my English teacher started in on both, and I realized that the poem and the story have a lot in common.  The other thing that I noticed is that both items have bleak and depressing messages.  
The poem ends with the following four lines.  

Not one would mind, neither bird nor tree,
if mankind perished utterly;
And Spring herself, when she woke at dawn
Would scarcely know that we were gone.

Basically, Teasedale is saying that nature itself could care less whether or not mankind walks the surface of Earth.  Nature will carry on its business.  It doesn't need humans and will barely even notice our complete absence.  That's sad.  When a reader compares that message to the full story, then a reader realizes that Bradbury's message is the same.  Mankind (at least in Allendale) has been wiped from the face of Earth.  The house goes about its business as if people were in it.  The house does ask the missing people questions, but the house eventually just makes its own decisions.  Ultimately, it doesn't need the people to operate.  As the story ends, the house is dying.  Nature is taking it back.  Nature will be taking back the entire city.  Given enough time, the processes of ecological succession will ensure that all traces of human habitation are erased.  Both the story and the poem point out the fact that the world is perfectly capable of going about its business without humanity in it. 

What do noble Romans, such as Cassius and Flavius, fear or resent about Caesar's successes in Shakespeare's Julius Caesar?

Early in act 1, scene 2, of Shakespeare's Julius Caesar, Cassius and Brutus express fear that Caesar will be made king, leading to the fall of the Roman Republic. They express their fear when, at the games, they hear the crowd calling for Caesar to be made king and soon learn thereafter that Antony had offered him a crown three times. Though Caesar rejected the crown all three times, the Conspirators feel that he was loath to reject it as a result of his rising arrogance and soon may not reject it.Cassius takes his fear one step further when he recounts a story in which, while crossing the stormy Tiber together, Caesar nearly gave up in exhaustion and called out to Cassius, "Help me, Cassius, or I sink!" (1.2.111). In Cassius's view, the people of Rome now think of the weak and frail man Caesar as a god. Cassius revolts at Caesar's arrogance and is jealous at the thought of having to bow before Caesar, jealous of Caesar's power. We particularly see Cassius express jealousy over Caesar's power when he asks Brutus the following, upon hearing the people shout in exultation as more honors were bestowed on Caesar:

Brutus and Caesar: what should be in that "Caesar"?Why should that name be sounded more than yours? (1.2.142-43)

The conspirators are jealous of Caesar's power because they know that if he is made king, their roles as senators in the Senate will be rendered powerless.Similarly, like all the conspirators, Flavius is jealous of Caesar's power and wants to protect the Senate from Caesar's dictatorship. While Flavius is not in the play much, in act 1, scene 1, we see him and Marullus chastise commoners for wanting to pay honors to Caesar on Caesar's holiday. They chastise them by calling them hypocrites through pointing out that they paid the exact same honors to Pompey who has now been slain by Caesar. Their point is to assert that if they honored Pompey, then surely they can't legitimately honor Caesar who has killed Pompey. Flavius then commands the commoners to gather themselves together by the banks of the Tiber to weep for the fall of Pompey. We can deduce based on this that Flavius was a strong supporter of Pompey as a protector of the Republic and now fears that Caesar will destroy the Republic.
https://www.ancient.eu/article/803/the-murder-of-julius-caesar/