The truth is that before the big bang, we do not know what was there. Physics cannot tell us that, because the laws of Physics were created at the point of the big bang. Here will have to resort to Philosophy. However, there are Physicists and mathematicians who are working on ideas that get round this problem, but there is still a large dose of philosophical arguments in their reasoning (M-theory, string theory etc). At the exact moment of the big bang, there was an infinite amount of energy (hence big bang!) present. We know this. What we do not know is where this energy came from, or what caused the big bang or even if there was a "before" (time was also created in the big bang).
Space-time is one of those concepts that is still not fully understood (to the best of my knowledge), and yes you are right, it is everywhere - it goes into the aforementioned string and M-theories. I know very little about these - I haven't read enough about them and I don't know the mathematics.
As to your first question above, the theory or model is an attempt to put the thing we are trying to describe into terms that we can understand. Some theories describe very specific things, for example a simple spring-lattice molecule, where all the molecules are connected by "springs" can be used to describe some solids, like ice, but this doesn't fit in with Quantum mechanical descriptions of the same solids. This is because although the spring-lattice model describes simple beahviour well, it is too simple to describe more complicated behaviour, and is a "coarse-graining" of the more detailed model to allow us to understand it more clearly.
Most physical models are continuously adapted and modified to represent new discoveries and findings.
When two theories are said to contradict each other, then it is generally because they are two established theories that are well grounded and we haven't worked out how to combine the two. This is sometimes very difficult, which is why a Grand Unified Theory (Or Theory of Everything) still eludes us.