The questions that follow the primary question are rhetorical questions. They are asked for effect and the answers are understood: "yes." (Using rhetorical questions is a very effective persuasive technique.) By creating this catalog of rhetorical questions, Hughes presents the various terrible consequences that result from dreams being frustrated or postponed. He saves his strongest question (and strongest consequence) for the poem's conclusion. Since racism was both an entrenched social and political evil during Hughes' time, his poem addresses both.
I don't think that Hughes actually answers his main question because he is simply trying to get his readers to ask this question themselves. He does subtly direct what the answer to his main question might be because all of his following questions carry a negative connotation. The structure of his poem--following a question with other questions--is actually similar to Socratic discussions. Hughes starts the "discussion" with his main question--"What happens to a dream deferred?"--and then allows the reader to start asking his own questions about the theme.
In answer to your second question, the poem addresses both political and societal values. The politics of Hughes' day caused the social problems that suffocated the dreams of many African-Americans.
Part of what makes Hughes answering a question with more questions is that the topic matter he is exploring is so multi- dimensional. When he ponders about "What happens to a dream deferred," Hughes is asking a powerful question about what happens when dreams die. There is ample discussion about how to accomplish dreams, or what happens when you achieve your dreams, but there is little about what happens when dreams are set aside, denied, or promised and then stolen. This becomes a critical question for so many people of color in American History, a nation where freedom and opportunity is embedded in its founding and origins, but seems to have such challenge in delivering it for all of her children. Hughes' exploration of this topic in imagery makes for an extremely compelling understanding about the nature and breadth of the deferral of dreams. The last image is one of ominous foreboding, almost to suggest that individuals who defer dreams might have to deal with some rather unpleasant truths on both individual and social levels: "Or does it explode?"