It's a big place—in real life and in Dunbar's poem. The world also has a responsibility to recognize the suffering that occurs not just in a personal sense, but a worldly one too. Unfortunately, the "world" often ignores the kind of suffering that doesn't immediately affect it (specific people/places). But by keeping things universal thematically and stylistically, the speaker is suggesting that it's all connected. So ignoring problems doesn't keep them away.
Lines 6-7: The rhetorical question we get here is directed at the "world." And since it has a slightly sarcastic tone, we get the sense that the world is acting mighty ignorant and cold towards the suffering of black Americans.
Line 14: The world is allowed to "dream otherwise," which just like the previous lines suggests that the world is behaving kind of like a child. It's dreaming instead of getting real. So the speaker is saying it's time to wake up.