Please respond to the following questions: What do the portrayals of Walter Lee and Beneathea In “A Raisin in the Sun” suggest about identity within the Black community during the late 1950's? How would you describe the tone of Dr. King's "A Letter from a Birmingham Jail"? Do you think his tone is effective given that he is addressing a white audience? What does Malcom X mean when his says it is either the ballot or the bullet? Why does he think Black Nationalism is the solution to the Black community's issues? Why is poetry not a luxury for Audre Lorde? How might Black women find it a useful tool? What is the "Black Aesthetic"? In your opinion does this aesthetic empower or hinder Black writers during the Black Arts Movement? What is Alice Walker saying about Back women's creative expression? Why must we acknowledge this creative expression for what it is?

This question covers a lot of ground. Let's go through each of the six prompts and discuss how you might answer them, citing a few useful examples to help you craft your own responses.
1.   A Raisin in the Sun. There's a lot to say about these two characters in the play and what the playwright, Lorraine Hansberry, shows the audience about Chicago's black community in the late 1950s. Both characters are ambitious and forward-thinking, dreaming of better things for themselves and their family. The family has recently received an insurance payout after the death of the patriarch, and there's disagreement about what to do with the money. Walter Lee wants to help the family rise up out of poverty by investing in a liquor store. Beneatha wants to go to medical school, even though her brother doesn't think it's a realistic dream. Her sarcastic response shows Beneatha's defiance of her brother:

And forgive me for ever wanting to be anything at all! (Pursuing him on her knees across the floor) FORGIVE ME, FORGIVE ME, FORGIVE ME!

Despite their differing views, neither character wants to continue the cycle of poverty. These are modern characters, and they represent the aspirations of young black Americans coming of age in mid-century America. 
2. "A Letter from a Birmingham Jail." This open letter was also called "The Negro is Your Brother," which gives us a clue about the tone. Though the letter is an argument, King's tone is warm and conciliatory, not aggressive. Right off the bat, and throughout the speech, King attempts to find common ground with a white audience both in content and form. He addresses his audience as “My Dear Fellow Clergymen" and "my friends."
3. "The Ballot or the Bullet." Malcolm X's speech was addressed to an African-American audience. He urged them to exercise their right to vote for politicians who would represent their interests (and civil rights in general). But there's another layer to the speech that's intended for a wider audience. If the African-American population continues to have their rights curbed by legislation and discrimination, he warns, they'll have to resort to another form of power (the bullet). His point isn't only about race. It's about human rights. He believes that black people must come together to fight corruption and oppression:

Now in speaking like this, it doesn't mean that we're anti-white, but it does mean we're anti-exploitation, we're anti-degradation, we're anti-oppression. And if the white man doesn't want us to be anti-him, let him stop oppressing and exploiting and degrading us. 

4. Audre Lorde herself answers this question best:

For women, then, poetry is not a luxury. It is a vital necessity of our existence. It forms the quality of the light within which we predicate our hopes and dreams toward survival and change, first made into language, then into idea, then into more tangible action. Poetry is the way we help give name to the nameless so it can be thought. The farthest horizons of our hopes and fears are cobbled by our poems, carved from the rock experiences of our daily lives.

For Lorde, poetry isn't a "luxury," which is to say it's not something that would be nice to have but isn't quite necessary. It is an essential form of expression, especially for women and moreover for black women, whose voices aren't always heard. Poetry is a platform for expressing important ideas and thoughts that would otherwise stay inside people.
5. "Black Aesthetic." Many art critics and scholars believe that the development of a Black Aesthetic, an art movement that went hand in hand with Black Power, was essential to the development of African-American artistic tradition in the late 1960s. The Black Aesthetic introduced many important African-American figures in music, art, and culture to a wider audience, as their faces and figures were represented in murals; public artworks, like those murals, helped foster a sense of community among black artists and the neighborhoods they lived and worked in. 
This question asks for your opinion, so it's up to you to decide. 
6. I'm not sure if you're referring to a particular text here, so let's talk about Walker's views in general. She invented the term "womanism" to describe "black feminism," as she believed that feminism (as it was originally defined) did not include or fully encompass the perspectives of black women. Clearly, her advocacy for black women, whether in or out of a creative field, is important to her work.

No person is your friend who demands your silence, or denies your right to grow.
The most common way people give up their power is by thinking they don't have any. 

Some of her most frequently cited statements, like the two above, speak to her belief in the importance of black women (and of all women, and all people) to express themselves—and why those expressions shouldn't be censored or edited for any purpose. She demands equality for black women, and urges them to demand it for themselves.