Anne Melton was Laura's cousin, not sister. There is no evidence of which of them (Melton or Dula) killed LF, but Tom confessed. He almost certainly did help with the body.

Grayson was not a Sherriff at all, but a local landowner who had been a Colonel and then a Major (it was not a bust, he transfered to a different unit and got a different commission); he had retired a Major and was known as Major Grayson. Tom Dula, in fleeing, found he needed new boots, and stopped at Grayson's, working for the Major until such time as he could afford the boots. Then he took off.

Soon thereafter, a posse arrived at Grayson's place looking for Dula, and they found him and took him back to North Carolina, where he confessed and was hanged.

Although he was almost certainly guilty, the extradition across state lines was not legal. If it happened today, he'd be freed on a technicality.