I heard a Negro play (3)
The speaker is telling his audience, that he heard the musician play. Don't people usually say that they saw a band? The speaker is engaging with the musician through sound, and the reader has to engage both through sight (reading).
He made that poor piano moan with melody (10)
A great musician can carry on a whole conversation with his instrument. Jazz musicians do this all the time. This musician is a virtuoso, meaning that he has total mastery of his instrument.
"I's gwine to quite ma frownin'" (21)
By writing in dialect, Hughes is communicating on an unusual frequency. This might put off some readers. If you struggle with it, just read it out loud, because it is spelled phonetically (according to sounds). The thing to take away here is that language provides a lot of room for improvisation, and breaking the rules of Standard English can show you the way towards new forms of self-expression.