Does Planet X really exist?
No, as described in your question, not only does it not exist, but cannot possibly exist. The people making up these stories clearly have no knowledge of orbital mechanics or even general astronomy. Sure, the Earth will one day come to an end, but not for billions of years. The people who make up these stories usually have a book or a TV show to sell, but no real knowledge of, or background in, the physical sciences. Exactly the same applies to all those exceedingly dumb 2012 stories. In mathematics, “X” is sometimes used to denote an unknown factor, and in the past, astronomers have used the term as a reference term for something they have yet to confirm. Before Pluto was discovered formally by Clyde Tombaugh, astronomers knew something was perturbing the orbit of Uranus, and used the expression “X”, really for want of a better term. Once Pluto was discovered and named, the term Planet “X” was dropped.