Comment on the answer given by pohnpei397:

It seems to me that the murderer is not the narrator, but Uncle Caesar.

The dead Caswell is clutching something in his hand.  When he finally drops it, the narrator picks it up and pockets it.  Later, when the narrator is riding away from Nashville, he examines the object.  It is a "yellow horn overcoat button the size of a fifty-cent piece, with frayed ends of coarse twine hanging from it."

This is the unique button that the narrator noticed, near the beginning of the story, on Uncle Caesar's coat.

Uncle Caesar, who always tried to take care of Mrs. Caswell, has murdered Caswell, who always steals her money.  The narrator, who sides with Uncle Caesar, takes the evidence (the button) and destroys it by throwing it out of the train window.

I'm not quite sure what you are asking here when you say "and them and characters..."

The story is told from the point of view of a man who has come to Nashville to sign Azalea Adair to a contract.  He works for a magazine that wants her to write for them.

The main characters are

• The narrator
• Uncle Caesar, a black carriage driver and former slave
• Azalea Adair
• Major Caswell -- the villain of the piece.

The basic plot is that Caswell is married to Adair and is living off what money she can get.  Much of her money comes from Uncle Caesar, who belonged to her father.  The story ends with the narrator killing Caswell because he is causing Azalea and Caesar so many problems.