It would be highly surprising to find objects approximately the mass and density of the Earth within the Kuiper belt; we might not be able to see a low albedo object, but the gravitational perturbations should indicate its existence. Trans-Neptunian Objects (TNO) further out in the scattered disk are possible but tend to be contraindicated by accepted theories of solar system formation; an object as massive as the Earth would be unlikely to be thrown into a long orbit by coupling between two planets (even Jupiter and Saturn), and its periodic return should wreck havoc with the existing stability of smaller worlds or Jovian moon systems. It might be that such an object was drawn out by some type of long period “Nemesis” object, but no such partner has been found to date, and if it did exist it may be thousands of AU outside of the main system; barely a part of our Solar System and easily perturbed by outside forces. In short, if there are any Earth-like worlds out there, they’re probably too far to be seen or of any use.
Regarding Earth-like worlds around other systems, given the vast number of stars it seems almost certain that they exist, and even quite possible that planets of the approximate size and composition are common. However, a world with conditions that are livable for us is much less likely; we have only a rudimentary understanding of the development of Earth, but it is clear that just being within a habitable zone isn’t of itself sufficient.