Anti matter elements?
There is no theory, nor is there a need for one. To put in in other words: yes, there is a theory, and that's the one you are already familiar with. Antimatter elements are precisely the same as ordinary matter elements, only the other way around. There "are" (read: "could be", though some were actually detected) antihydrogen, antihelium (all with the same energy levels as their real counterparts), also anticarbon, antiwater, anti-$\ce{NaCl}$, antiglucose, and pretty much everything anty-else.

To compose a substance of particles and antiparticles together is an entirely different question. Yes, there is a compound of electron and positron; it is called positronium and has the lifetime of a few microseconds or something. Electrostatic forces attract the opposite particles, rather than repel them (otherwise it would not be a compound, BTW), so it annihilates pretty quickly. There are other similar compounds, equally or more short-lived. Matter and antimatter do not sit well with each other; there is no going around it.

As for the spots of the Universe composed of antimatter, there was once a mainstream view that there must be many of those, about as many as those made of matter. Then the global symmetry broke, and things went... complicated. I'd rather leave it at that. Go ask at Phys.SE for a more comprehensive take.

So it goes.