In Microcosm, CERN's science centre

What is the basis of strings theory and what is a parallel
Universe?

String theory is a theory that attempts to describe all particles (like electrons, quarks, etc.), and the four interactions between them (gravitation, electromagnetism, and the weak and strong forces), in a unified framework. The idea is that elementary particles are not really point-like, but rather small loops of vibrating strings. In fact, the theory proposes that the different matter particles, and the particles that mediate the forces between them (graviton, photon, the W and Z bosons, and gluons) are just different oscillation modes of a unique kind of string. Hence all particles and interactions are described in a unified fashion.
String theory implies that there are six additional spatial dimensions. Since these have not been observed, one is led to the conclusion that these extra dimensions are curled up (or compactified) and have a very small size, so that they are not observable in our daily life, or even at the most precise present experiments. In some models, the size is very small and it is difficult that we will ever have direct evidence for them. In other models, the size of these dimensions is far larger and could be observed in future accelerators.

String theory has a fascinating but very difficult mathematical structure, which involves the study of the geometry of the six extra dimensions. For instance there seem to be many possible ways to curl up the extra dimensions, by choosing different shapes and sizes, leading to very many different string models. Unfortunately, the mathematical and conceptual difficulties of the theory, and the seeming arbitrariness in choosing the structure of the extra dimensions, have for the moment prevented researchers from obtaining concrete experimental predictions of the theory, which could be compared with future experimental results.

For more information, see http://www.superstringtheory.com/

About parallel universes, there are several possible meaning for this
expression. You may be refering to the fact that in some string theory
models, familiar particles are described by strings which are localized in
a subspace of spacetime (a slice of a larger universe), while gravity
propagates through the whole spacetime. Different slices
would be analogous to different parallel universe, which can interact with
each other only through gravity.

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If antimatter exists for all things, what can be the antimatter for a string?

In string theory, particles are oscillation modes of strings. Antiparticles are strings in the opposite oscillation mode.

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Do strings vibrate with respect to time ( is the equation governing them is time dependent)?

 

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String theory postulates extra dimentions which are obviously not experienced by us. One solution appears to suggest that these extra dimentions are tightly coiled in the same order of size as the strings themselves. How does this not conflict with the General Theory of Relativity & produce a massive gravitational field?

In string theory the extra dimensions are indeed curled up and have a very small size. However, the graviton is still massless, and propagates in the infinite size dimensions. The interactions of this massless graviton with the massive particles is exactly as in the theory of general relativity,
so there is no contradiction.

On the other hand, it is true that, because of the small extra dimensions,
the theory contains additional particles, which are partner of the
graviton (known as Kaluza-Klein replicas) which are very massive. It is
possible that these extra particles (which are not involved in the
gravitational interactions) can be experimentally observed in future
experiments.

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