Can you give me some ideas about this critical essay topic: What ideas does Tennessee Williams, in A Streetcar Named Desire, suggest about an individual's attempt to secure satisfaction or self-fulfillment? Can you also give me some quotations which are related to this essay topic? There is some additional information in the photo I provided.

As your assignment sheet suggests that you will need to write an outline as your first step, this response will address how you might structure your outline and essay.
Introduction: You might argue that each of the characters presented or mentioned in the play strives towards some degree of self-fulfillment and either succeeds or fails to a greater or lesser degree. However, these goals often come into conflict with the needs of other characters. For example, Blanche's desire for gentility clashes with Stella's desire for a happy marriage with Stanley. In your introduction, you should mention that in the body of your essay, you will write one section about each major character.
Allan Grey: Although Allan, whose suicide happens before the start of the play, does not make an onstage appearance, he is an important figure in the plot. As the gay husband of Blanche DuBois, Allan struggles between his desire to express his true sexuality and his desire to conform to social norms. 
Blanche DuBois: Her desire to return to the life in Belle Reve is in conflict with her present reality and also brings her into conflict with Stella and Stanley.
Stanley Kowalski: His main desires as a character are for sexual fulfillment and respect. This brings him into conflict with Blanche (whom he rapes).
Stella Kowalski: Stella is the abused wife of Stanley, who desires a traditional family and also has a strong sexual desire for her husband. Her sense of family leads her to take in Blanche, but she is caught in the conflict between Blanche and Stanley.
Quotations:
“I don't want realism. I want magic! Yes, yes, magic! I try to give that to people. I misrepresent things to them. I don't tell the truth, I tell what ought to be the truth. And it that's sinful, then let me be damned for it!” 
"When I was sixteen, I made the discovery - love. All at once and much, much too completely. It was like you suddenly turned a blinding on something that had always been half in shadow, that's how it struck the world for me."