Well, Death got his revenge on two of the three brothers, the brother who was given the Elder Wand and the brother who took from Death the Resurrection Stone. The third brother, who took Death's Cloak of Invisibility, was able to elude Death until he himself, the third brother, chose when he was ready to die.
But though Death searched for the third brother for many years, he was never able to find
him. It was only when he had attained a great age that the youngest brother finally took off the Cloak of Invisibility and gave it to his son. And then he greeted Death as an old friend, and went with him gladly, and, equals, they departed this life.
Tales of Beedle the Bard - pages 92-93 - Bloomsbury - The Tale of the Three Brothers
Death is last seen guiding the third brother from this life; the story does not say where Death and the third brother will be going. Canon does not address why Death never reappears in any of the seven Harry Potter books and I personally don't know of any source that answers that question. Perhaps someone else will have the answer.
Yes, in the story The Three Brothers, Death is meant to be Death. However, it is up to the reader to accept or reject this as true.