If the universe is expanding, what is it expanding into?
When the big bang happened where did it occur?
When the big bang happened how did it occur?
Where did the energy come from? Energy can not be created or destroyed does that mean, energy has existed before the universe was here?
1. If the universe is expanding, what is it expanding into?
The universe isn't expanding into anything. Space-time isn't curving into a higher-dimensional space. So what do we mean by "curved" and "expanding", words usually having a meaning only for objects in space?
The answer is it is just an analogy. Mathematicians have found properties of space an ant on a surface would see in his world and generalized them to higher dimensions. For example an ant could choose three distant points on a sphere and connect them by lines he believes to be straight and non-curving at every point and find out the sum of angles inside such a triangle is larger than $180^\circ$. If we do this in our space and find out we also get a triangle with more than $180^\circ$ inside, we woud say we live in a space with positive curvature. We just define it that way, just by analogy. And we need not believe there is another space embedding ours.
With an expanding space the matter is similar. On an expanding sphere, the ant would go around places and find them to be farther and farther apart. By this analogy we define an expanding space as a space where all the distances grow in time. Again, we do not need our space to be plunged into something else to expand in this sense. For the studies of the early universe the "smallness" of the universe has a very clear sense - it means that things that are now far away were very closely packed by physical interaction and they could easily reach out to each other.
However, there are some subtleties to this, for example because galaxies and other gravitating objects act basically as a pin which holds a chunk of the sphere from expansion. You can see that this gravitational "pin-down" is basically holding by the Newtonian gravitational force.
How do you then simply tell between galaxies flying away from each other by inertia and some repulsive force and space expanding between them? The answer is you don't. You could understand the metric, the notion of space-time "distance" of general relativity, as a peculiar field acting on all physics in a flat space, e.g. making signals and particles fly faster, and all the observations would be without a change. "When the physics don't change, the physicist don't care."
General relativity includes non-trivial topology, but it does not "predict" it in any local sense from the configuration of sources - the field can be only sometimes inconsistent with the configuration and topology. Hence, you could say the whole "curved space-time" is just a word we use in analogy to some formal structures on actually curved objects. It is just a handle to get to the real physics and as long as no ambient space with extra dimensions contributes to the physics, we say it does not physically exist.
2. When did the Big Bang happen and where did it occur?
"When" we do not know. The physics of the very very early universe are unclear and so we do not know if the Big Bang in the sense of "the universe coming into existence" even happened. We do however know that if we extrapolate general relativity backwards in time, we reach a point where all places in the universe approach extremely close to each other (in the sense of the "metric") and just a tad deeper into the past the equations break down. This point would be about 13.8 billions years ago.
In the old sense of general relativity, the Big Bang would have happened everywhere. All the places would just be so close together that distance between them is eventually zero. They might still be distinct points in space, but they are all in seamless physical contact. The equations do not allow to go further back into the past, so you might say it is a "beginning of time".
But you could also jump to the conclusion the whole universe grew "from one place" or from a "primeval atom" - but this is exactly an extrapolation towards the breakdown which is done more religiously than physically, as might have been partially the case of the catholic priest Georges Lemaître, the pioneer of Big Bang cosmology. It works pretty well for a finite universe because it's volume shrinks to zero in this process, but for an infinite one (which might be the one we are in), the universe is infinite at every point before the breakdown - amongst other properties, it has always an infinite volume. How would it jump to a point from there? The equations just do not give a clear explanation and we cannot expect them to, since they are full of undefined quantities at such a moment.
Nowadays we are very sure it did not happen the way general relativity describes it. We are just pushing the boundaries of our knowledge further and further back in time, expecting the universe to be shrinking more and more but without knowing where this will take us. We talk about "cosmological models" rather than "cosmologies" because we know it is a foolish ambition to formulate a definitive "cosmology". We just do not know what might be hiding behind the corner.
The Big Bang is now more of a reference either to the point we know the distances between places to be the smallest or to the point in time where general relativity originally predicted the breakdown. So in a sense, it is nowadays a reference to an era of the whole universe - the Big Bang now refers to "everywhere" in the universe about 13.8 billion years ago.
3. How did the Big Bang occur? Where did it get it's energy?
Once again, we have no idea. Current physics can tell you what happens based on initial conditions. It cannot tell you why a particular set of initial conditions is realized apart from extrapolating further and further into the past. Certain areas of research try to give a holistic description which would for example say that according to some very basic principles, the laws must have been this way and only one set of initial conditions is allowed. I.e., the total energy in the universe would not be a part of the configuration but of the law. But as far as I know, none of these have yet brought any satisfying results in this question.
If there is a moment of "the creation of the universe" it could not be explained by anything outside because a working definition of "the universe" is "all there is". I.e., if something would explain the creation of the universe, it would be a part of the universe and might not be explained itself. You can create a closed circle of causes, but you then cannot explain why this circle is realized rather than not. This is getting philosophical and it is just a taste why physics really cannot provide an answer.
I.e. when you ask "Energy can not be created or destroyed does that mean, energy has existed before the universe was here?" you get into conflict with the definition of the universe being all there is. If there was energy before the universe then there existed something before the universe. But since the universe is the sum of all existence, the universe existed at that point - it existed before it existed. That is obviously a non-sensical conclusion. So if there exists a "creation point" of the universe, there is nothing beyond that just by definition. A statement of creation of the universe includes the statement that energy was indeed created at such a point.
A half-answer to your question might lay in some of the cyclical cosmological models which model the Big Bang as formed from a seed of a previous stage of the universe. Many of these models talk about a "bounce" of the previous universe almost collapsing and then stopping to reexpand - this is usually caused by quantum-gravity effects. The energy it has would be provided by the previous universe and the Bang would be a "Bounce" fully understood by physical laws.
Nevertheless, none of this answers questions of the type How did the previous universe gain it's energy?, Why is there something rather than nothing?, Why was this universe with it's laws and initial conditions picked rather than another one? Mainstream physics just does not provide an answer to these questions. These questions are beyond the scope of the usual scientific method and it might be just "by accident" that we find partial answers to them - there is no guarantee we ever will.
There are much better people to answer this question, but I will answer it from the point of view of an experimental particle physicist, the way I have filed this knowledge in my head.
Astronomical observations show that all clusters of galaxies are receding from each other, a behavior that refers to the effect of an explosion.
The theory of General Relativity, which treats gravity as a deformation of space-time around massive bodies, has been used to model this observation mathematically , the Big Bang is a particular solution within GR.
The BB in this theory happens from one point, as an explosion as shown in the links above. All points in our universe are this point. Practically metaphysical but true. So there is no meaning on "what it is expanding to", except mathematical: the functions necessary to describe the data show expansion of space. It is the expansion of the points within the universe that has been measured and modeled, without any reference to an "outside".
A useful for me analogy is the surface of a balloon. Our universe, in smaller dimensions, is like the surface of an expanding balloon. All points on the surface are receding from each other and as far as the surface is concerned, it just expands. All points on the balloon theoretically project back to the beginning point. Others like the analogy of a cake with fruit interspersed. As it rises in the oven each piece of fruit recedes from the others and if we could think that all of it could be originating from a point, all points in the expanded cake would be the beginning point.
GR theory differs from the Newtonian and special relativity world we have explored and are familiar with. For these we have definitions of energy and also conservation of energy.
In the GR framework there exists energy but the concept of conservation of energy is not valid. Energy can appear according to the appropriate equations. GR is necessary in the description of observations of large dimensions in space and time and very massive bodies. Energy conservation is not a general law in GR, but is observed locally.
As for when the big bang happened, in the links I gave you one reads out the measurement as 13.8billions of years ago. Astronomy has measured this. Where has no meaning in the BB model that agrees with observations up to now, because all points in the universe were one point, according to this model, and no reference is included to an overall higher dimensional system ( as in the balloon analogy where the third dimension outside the surface exists). It is all a mathematical model.
The space started expanding in accordance with GR expectations, each point receded from each other point. A detailed exposition of the model should include that the real beginning is shrouded by quantum mechanical effects. General relativity is a classical theory. It is expected that at the projected back singularity of the BB the quantum effects are dominant , and quantum mechanics does not have singularities . There are effective models for this necessarily quantized period of the BB as shown in the figure referred to above:
The BB model fits the observations up to now.
Energy conservation is funny with general relativity. To have a conservation law you need something which is a constant of the motion. In the case of energy in spacetime this requires there be a Killing vector that is constant along all timelike geodesics. This isometry is what defines the conservation of energy. Spacetime metrics for cosmologies do not admit a Killing vector which is constant along timelike geodesics.
The universe expands as a manifold. The spacetime is foliated by spatial surfaces, where points on that surface increase their distance along the time direction of the foliation. If the universe is flat these spatial surfaces are just $R^3$ spaces, and the curvature of spacetime is defined by their extrinsic curvature in the space plus time = spacetime. The universe is not particularly expanding into anything outside of itself.
Your assumption that there has to be something before, after, outside or even in between, some sequence of events, while natural to classical Physics, is not necessary. Google for “Lucretius arrow "edge of the universe"” finds various web references, none of which I particularly want to cite, to the fact that Lucretius asked what happens at the edge of the universe around 100BC. With various similar search terms, Google leads to various Philosophical forums that have had similar Questions asked.
Your Question also has slight similarity to the ancient Zeno's paradox of the Arrow.
AFAIK, there is no settled Answer to this. It's often convenient in mathematics to assume that there's a continuum, and such models can be quite effective, but there's no necessity. Taking things to be without end, infinite, in endless ascents or descents, etc., while often useful, also requires care when constructing mathematical models, because without care things can end up being badly defined.
To step into the detailed Question you put, you are asking about before, after, and outside what we can confidently infer from fitting experimental data to models of current physical theory. There does not have to be anything at all there. A different possibility, perhaps equally disconcerting, is that we may be using models of the scientific theories that we find to be very accurately consistent close to Earth and the Sun in a domain in which the the experimental data does not fit any single consistent model. In particular, there is no guarantee that there is a consistent atlas of the big bang (and yes, for those who know of these things, I also mean this technically, as of a manifold).
I fear that this is rather general, but insofar as I see the Question blows Philosophical so blow I.
Only a physics undergrad here, so I only know of this stuff cause ive done a bit of extra reading, perfectly possible that I misunderstood it. But you can "create" energy/matter, the catch being that you must also make a matching amount of anti matter/energy, resulting in a net gain of 0 energy/matter. Something I saw before I learned this that kind of started my understanding of it was this video on Hawking radiation http://www.youtube.com/watch?v=S6srN4idq1E
If I understood the reading correctly, this is a possible mechanism of creating the universe (particle/anti particle mechanism). This apparently happens all the time in Quantum Mechanics, but on a much smaller scale, and apparently the only way to use this effect to create something that lasts more then a fraction of a second is to have it create a universe worth of matter/energy and matching anti matter/energy. What makes this so hard to get a definite understanding is the fact that you have to apply general relativity as well as Quantum field theory, and the 2 can sometimes disagree (I don't have enough understanding of either to say exactly what the disagreement is, I just know there is apparently one)
BECAUSE WE MEASURE WITH ATOMS (or atomic properties) a change in the measured value can be either a true change of the observed quantity or a change in the properties of the ruler (the atoms).
I'll revert the paradigm the space expands to this one: the atoms are shrinking
THEN I have simple answers :
(*) A newly created particle at LHC is detected by it's spreading field.
Here I show that there is no way to distinguish between the spectrum of a scaled atom and the one in motion (redshift) and that the atomic properties are self referenced, i.e. they scale naturally.
With my version I've a cause for the measure of the space expansion and I have NO need of: BB, Inflation, Dark energy, Dark Matter. To explain the evolution of the universe only one parameter is needed $H_0$ as is showed in this formal papper A self-similar model of the Universe unveils the nature of Dark Energy, with my modest contribution. (This doc is not peer-reviewed, but if you think that anything is wrong with the paper, I can answer to any objection to it's content.)