Refractive properties of materials? I've just read this article about meta-materials with 0-refractive index, which potentially may "permit" light with super-luminous rate /under rate is meant the propagation of light's phase, which doesn't transmit information => there is no valuation of the laws of physics/.

Generally speaking, the refractive index of materials depends on the (dominant) molecular interactions within them, on their morphous structure, etc. As you know, these molecular properties govern lots of other chemical features like the viscosity, the density, to some extend the aggregate state, and so on... On this account, it should not come as a surprise that there exists a clear correlation between the refractive index and the properties, mentioned above - e.g. fluids of higher density tend to have higher refractive properties; same goes for viscosity; and so on... Based on those remarks one is able (at least) to guess how they can improve / worsen the refractive index of a given fluid - discussed for instance in this research on aerosols.

My question, though, is how does the refractive index of alloys, polymers, crystals, and solids in general relate to their other chemical properties?

Furthermore, is there a way at least to guess what materials one should potentially try to use in order to create / synthesize a meta-material, like the one from the article, that breaks the limits?
I can only answer your question about the relation between refractive indices and other properties with two examples.

When looking at dispersion interactions between particles in solution the Lifschitz Theory connects the refractive indices with the Hamaker constants.
The information about refractive indices is even used to choose materials in a way to cancel out dispersion interactions between particles of different kind. (I will attach a paper URL in the next days, just heard it from our professor in the lecture)

Another application of refractive indices is X-Ray NEXAFS spectroscopy and  many more spectroscopic methods involving electron or high energy light radiation. By the Kramers-Kronig relation it is possible to connect absorption constants and refractive indices. Especially one can find for example absorption edges.

Then here I found some probably interesting papers regarding your question. At least their references will be a good starting point. Unfortanetly I have no access and could only read the abstract: 

http://www.sciencedirect.com/science/article/pii/0020089165900205

http://www.sciencedirect.com/science/article/pii/0032395083902836