In the known universe, would an atom not present in our periodic table exist? I have watched this movie Battleship. In it the researchers say this piece of metal is alien because we cant find this metal on earth.
So that would mean somewhere else in the universe any of the following should be true?


*

*Atoms' composition is not similar to that as on earth (nucleus, electrons, anything else)

*Elements with atomic numbers above 120 or 130 are stable (highly impossible without point 1)

*The realm itself is observed by different binding forces (but then, once that elements realm has changed, it should become unstable and collapse)

 A: In fact, some nuclear theorists do believe that there will be relatively stable heavy elements, as per your point 2. The so-called Island of Stability is predicted to occur because stability is maximized at certain so-called magic numbers which correspond to especially stable isotopes when the number of protons and/or neutrons matches one of the numbers. In particular, Z=114, 120, and 126 may have long-lived isotopes. These haven't yet been produced because it's difficult to get to the requisite number of neutrons to achieve a stable nucleus.
I should emphasize that this is just a hypothesis with essentially no experimental evidence at the moment. It is, as far as I know, a fairly active area of research. It almost sounds like crackpot science, but it definitely isn't and has a number of notable physicists and chemists connected to the hypothesis.
It is nonobvious whether these would be metals, though. If all you want is exotic metals, you'll have a much easier time just making compounds that haven't been synthesized on earth.
A: Metallic hydrogen is a metal that's not found on earth (but may be present in Jupiter): http://en.wikipedia.org/wiki/Metallic_hydrogen
Wether it does anything but evaporating or burning at ambient temperatures and pressures (or whatever conditions those aliens encountered in this movie), I don't know.
Since metals a generally in the lower left corner of the periodic table, I see no other candidate except transuraniae. 
Of course, the alien metal could be handwavium, a material traditionally used for filling up plot holes.
A: Well, meteorite minerals like iridium and all aren't really found on Earth in appreciable quantities.
What you're looking for are exotic atoms. These certainly exist, but are too unstable. And, for certain exotic atoms like onia, atomic number isn't even defined.
The binding forces cannot be different since the coupling constants are...well... constant (not sure what string theory says about this--but the Standard Model keeps them constant).
One thing that I can think of are "satoms" (atominos?), made of sprotons, sneutrons, and selectrons. Or maybe some other superparticles. Supersymmetry predicts that each particle has a superpartner. These ought to exist in our universe, but we haven't detected any yet. They are a candidate for dark matter though.
I'm not too sure of how superparticle stability works, though. Seems like only one of them is stable. We could make an atom out of that, I guess. But it's electrically neutral, and probably very light. So there may or may not be sufficient force holding it together.
As @annav said, what you may be looking for is a new alloy or something. THis will be an "exotic metal", but will still be made of normal atoms.
