Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Yup: Quentin says "I" in this story as he narrates, so that clearly makes it a first person tale. Whether he's a central narrator or a peripheral one, however, depends a bit on how you read the story.
He is a central narrator in that his perspective on racially divided Jefferson and his family's treatment of Nancy changes subtly throughout the tale. But if you see this as Nancy's story, Quentin gets downgraded to peripheral-narrator status.
Either way, Quentin doesn't converse much or express his feelings often. But he is hyper-observant, so we get clear narration of what is happening. Good job, Q.