What motivated the two towns to engage in the wall competition in "The Golden Kite, the Silver Wind"? What are the negative effects of the...

We're not really told why Kwan-Si first changes their
walls into the shape of a pig, but the messenger bringing the news seems to think that
by doing so, they have made themselves the more powerful town. A pig will eat an orange,
and so it looks like they are the town of strength. So, the Mandarin immediately orders
the shape of the walls changed to look like a club, to beat the pig away.
The towns prolong this competition because the town with the "strongest"
wall shape would be the winner, and therefore the more prosperous and successful
town. Think of it as a giant game of "Rock, Paper,
Scissors".

Because of this competition, the
townspeople have no time to tend crops or run businesses; instead they are constantly
building and rebuilding the walls. So, they fall ill, lose
money, and begin dying. Even the Mandarins are sick and weak at the end
of the battle. Because of their greed, and refusal to work in cooperation rather than
competition, their towns have suffered greatly.

What motivated the two towns to engage in the wall competition in "The Golden Kite, the Silver Wind"? What are the negative effects of the...

We're not really told why Kwan-Si first changes their walls into the shape of a pig, but the messenger bringing the news seems to think that by doing so, they have made themselves the more powerful town. A pig will eat an orange, and so it looks like they are the town of strength. So, the Mandarin immediately orders the shape of the walls changed to look like a club, to beat the pig away. The towns prolong this competition because the town with the "strongest" wall shape would be the winner, and therefore the more prosperous and successful town. Think of it as a giant game of "Rock, Paper, Scissors".

Because of this competition, the townspeople have no time to tend crops or run businesses; instead they are constantly building and rebuilding the walls. So, they fall ill, lose money, and begin dying. Even the Mandarins are sick and weak at the end of the battle. Because of their greed, and refusal to work in cooperation rather than competition, their towns have suffered greatly.

Why does Nora abandon her children in A Doll's House?

I'm not sure "abandon" is the right word for Nora's actions--we ultimately don't know whether Nora restores a relationship with her children after leaving Torvald or not. Nora does leave her husband at the end of Act III after she is forced to face his true nature and realizes how selfish he is. She also realizes that, as Torvald's wife, she has lived more of a child's life than an adult's. After her confrontation with Torvald, she most wants to reeducate herself to live as an independent woman. About her role as a mother, Nora says to Torvald:

"I am not fit for the task. There is another task I must undertake first. I must try and educate myself--you are not the man to help me in that. I must do that for myself. And that is why I am going to leave you now."

Nora's decision is not so much to abandon her children as it is to put herself first for the first time in her life. In addition to motherhood, Nora believes that:

"I have other duties just as sacred. . . duties to myself. I believe that before all else I am a reasonable human being . . . or, at all events, that I must try and become one."

In The Glass Menagerie, why did Laura give the broken unicorn to Jim as a souvenir?

Symbolically, the Unicorn represents Laura.  Once she has her romantic interlude with Jim, even though it doesn't work out, she feels changed, like the unicorn.

Technically, Laura becomes normal after she has been kissed by Jim, and like the unicorn, who now looks like a regular horse, can fit in with the other horses.  Laura has passed a threshold in life, she is changed by her experience with Jim.

"LAURA: Haven’t you noticed the single horn on his forehead?
JIM: A unicorn, huh? —aren’t they extinct in the modern world?
LAURA: I know!
JIM: Poor little fellow, he must feel sort of lonesome. 
JIM: Aw, aw, aw. Is it broken?
LAURA: Now it is just like all the other horses.
JIM: It’s lost its—
LAURA: Horn! It doesn’t matter. . . . [smiling] I’ll just imagine he had an operation. The horn was removed to make him feel less—freakish!" (pg. 86-87, Williams) 
  

Kindly name the 8 kings shown to Macbeth while greeting the witches for the second time.

When In Act IV Sc.1  Macbeth meets the witches  he  demands that they answer his question: "Shall Banquo's issue ever/Reign in this kingdom?" Initially the witches refuse but just before they vanish they remark, "Show his eyes and grieve his heart." immediately, "Eight kings appear, and pass over in order,the last with a glass in his hand; with Banquo following."

Shakespeare does not name the eight kings, because historically not much is known about Banquo, in fact some historians even doubt his  very existence! However in Shakespeare's own time King James I of England was believed to have been a direct descendant of Banquo. Macbeth's speech, "Thou art too like the spirit of Banquo.....And points at them for his" is thus meant to flatter the new Stuart King James I.

After Queen Elizabeth died childless, King James VI of Scotland a Stuart was crowned  the King of England as King James I. Two  coronations were held, one in Scotland where one  scepter was used and one in England where two scepters were used: "That two-fold balls and treble scepters carry." Scholars also interpret "treble scepter" to mean that King James' coronation united the three kingdoms of Scotland, England and Ireland. 

Thus, the eight kings would refer to all the monarchs of the Stuart dynasty who ruled England from 1603-1714. However,historically there were only six Stuart kings.

In The Mayor of Casterbridge, what is Michael Henchard's tragic flaw, and how can I describe it in a thesis statement?

Michael Henchard's heroic tragic flaw is related to
Hardy's theme of how a person's inner character traits interact with blind Fate. Hardy's
point is that for every choice a person makes, future choices are either broadened or
narrowed and Fate is either advanced or forestalled. An example of this is that early
on, Henchard resisted disencumbering himself of Susan and the baby, even though he
believed they were holding him back. With these moral choices, Fate was forestalled. Had
Henchard continued in this path of moral choice, Hardy suggests, his end in life would
have been a different one. Conversely, at the drunken moment that he agrees to a drunken
opportunity to sell Susan and their baby, Henchard makes a decision that so curses and
narrows his future choices that a blind destructive Fate is aided and hastened. It takes
some mental effort to keep the threads of Fate and Choice separate, especially when
Hardy is showing their interaction, but the message is that had Henchard displayed
different character traits, Fate would have brought forth different opportunities, or
the opportunities Fate did bring forth would have been rendered
powerless.

That being said, Henchard's tragic character
flaw is the dichotomy within his nature. He is honest to a fault as seen when he doesn't
deny the furmity woman's accusations. Yet he is also self-protective to a fault as seen
when he disencumbers himself of his family because they are holding him back and when he
lies to Newson by saying Elizabeth-Jane is dead.  He is faithful to his word and always
conducts his business on the highest standards. Yet he can explosively declare rash and
cruel things the pursue them as though they were reasonable and right things, again as
in the sale of Susan and the baby. He has determination and will power and can keep a
promise for years and decades. Yet he can't think with foresight and foresee disastrous
ramifications of impulsive thoughtless acts. He has a deep sense of justice, as in his
attitude toward himself when his is alone and forsaken at the end of his life. Yet he is
petty and mean spirited as was the case in his feelings toward the loving and accepting
Elizabeth-Jane the morning after the two paternity revelations. It is this unintegrated
duality, this combination of light and dark, that constitutes Henchard's tragic flaw:
though he has high values, he lacks the ability to think through and foresee future
affects of present choices and acts.

A good thesis
statement might incorporate this dichotomy and duality, this combination of light and
dark impulses, and relate it to Hardy's theme of interaction between personal choice and
Fate. Possibly something like this might work: Henchard's tragic flaw is the dark versus
light dichotomy of his nature that proves character-determined personal choice spurs on
or forstalls the realization of Fate.

In The Mayor of Casterbridge, what is Michael Henchard's tragic flaw, and how can I describe it in a thesis statement?

Michael Henchard's heroic tragic flaw is related to Hardy's theme of how a person's inner character traits interact with blind Fate. Hardy's point is that for every choice a person makes, future choices are either broadened or narrowed and Fate is either advanced or forestalled. An example of this is that early on, Henchard resisted disencumbering himself of Susan and the baby, even though he believed they were holding him back. With these moral choices, Fate was forestalled. Had Henchard continued in this path of moral choice, Hardy suggests, his end in life would have been a different one. Conversely, at the drunken moment that he agrees to a drunken opportunity to sell Susan and their baby, Henchard makes a decision that so curses and narrows his future choices that a blind destructive Fate is aided and hastened. It takes some mental effort to keep the threads of Fate and Choice separate, especially when Hardy is showing their interaction, but the message is that had Henchard displayed different character traits, Fate would have brought forth different opportunities, or the opportunities Fate did bring forth would have been rendered powerless.

That being said, Henchard's tragic character flaw is the dichotomy within his nature. He is honest to a fault as seen when he doesn't deny the furmity woman's accusations. Yet he is also self-protective to a fault as seen when he disencumbers himself of his family because they are holding him back and when he lies to Newson by saying Elizabeth-Jane is dead.  He is faithful to his word and always conducts his business on the highest standards. Yet he can explosively declare rash and cruel things the pursue them as though they were reasonable and right things, again as in the sale of Susan and the baby. He has determination and will power and can keep a promise for years and decades. Yet he can't think with foresight and foresee disastrous ramifications of impulsive thoughtless acts. He has a deep sense of justice, as in his attitude toward himself when his is alone and forsaken at the end of his life. Yet he is petty and mean spirited as was the case in his feelings toward the loving and accepting Elizabeth-Jane the morning after the two paternity revelations. It is this unintegrated duality, this combination of light and dark, that constitutes Henchard's tragic flaw: though he has high values, he lacks the ability to think through and foresee future affects of present choices and acts.

A good thesis statement might incorporate this dichotomy and duality, this combination of light and dark impulses, and relate it to Hardy's theme of interaction between personal choice and Fate. Possibly something like this might work: Henchard's tragic flaw is the dark versus light dichotomy of his nature that proves character-determined personal choice spurs on or forstalls the realization of Fate.