Eeks, you ask big questions! I can't answer it really, but I'll add some pointers and can only urge you to read about it as much as you can. We've only just recently had some exciting news from the scientific community http://www.bbc.co.uk/news/science-environment-26605974 regarding the gathering of evidence on the Big Bang, and every piece of the puzzle we can add brings us just that little bit closer to understanding it.
First thing to say is that you shouldn't think of the Big Bang as a "big bang" as it's misleading. It wasn't an explosion. The name actually originates with an astronomer called Fred Hoyle who hated the theory. It's one of those historical quirks that his nickname for it is how we've officially come to know it. Unfortunately it leads to everyone thinking it was like some giant pile of TNT going boom!
The Big Bang is really all about the expansion of space itself over time, from a single point without mathematical dimension called a singularity (these freaky things still exist in the universe as there's one at the centre of every black hole), right up to the vast behemoth multi-billion light-year universe of today. From the first instant to today, the energy contained within the cosmos has not changed. All that's changed is the space in which to put all that energy.
As Einstein discovered with E=mc2, mass and energy have equivalence so it's best to think of matter as being condensed energy. As the spatial dimensions of the universe increased, the immense energy of the initial big bang was able to fall to increasingly lower states.
The early universe was so small and compressed that it was simply too hot for any recognisable matter to occur. Even photons couldn't travel so all of space was totally opaque. At first it was a sea of super high energy gamma rays, but over time subatomic particles were able to form such as the recently discovered Higgs-Boson (thats why monster machines like the LHC are needed to discover such things - they need to recreate an instant of this intense heat as it was just moments after the big bang which is hard work!)
Then came the likes of electrons and protons forming first plasmas, and then finally the first neutral atoms. It took 360,000 years for the universe to get big enough and lose enough of it's density to allow the formation of atoms!
It is these first atoms which form the image now famously associated with the Big Bang.
http://scienceblogs.com/startswithabang/files/2011/11/101080_7yrFullSky_WMAP_1024W.png
That is basically a panoramic snapshot of the whole sky showing the density of energy at that moment when the first free hydrogen formed. It's the point at which space stopped being opaque, and photons were finally able to roam the cosmos as they do today.
Ever since then things have become less dense as the size of the universe increases. As in the laws of thermodynamics, heat seeks the lowest energy state it possibly can in a process called entropy. That simply put means, the bigger the universe gets, the colder it gets.
However things are yet to completely cool down yet. The temperature of space is still a few degrees above absolute zero, and that's not due to the warming effect of stars as it's constant throughout the whole universe. If you listen to a detuned radio playing static, or watch an old tv that's not tuned into a station, then about 10% of what your're seeing/hearing is the free energy still left over from the big bang.
Obviously we're all curious as to what will ultimately happen to this constantly expanding universe. Unfortunately the answer is pretty depressing. Entropy will always increase, until there's no free energy left. http://en.wikipedia.org/wiki/Heat_death_of_the_universe
As for the formation of stars, planets, asteroids - well that's all to do with other areas of study. The Big Bang is purely about the early moments of the cosmos. In short, gravitational pressure and electrostatic forces are responsible for the formation of heavenly bodies. All the Big Bang made was a lot of hydrogen (and a few traces of other light materials like helium and lithium).
We don't know why cosmic inflation (the process of the universe expanding rapidly) happened. All we can do is measure and record the evidence of it's having done so. We have a grasp of why it's doing what it's doing now, but that instant at which a singularity of incredible energy became a space with dimensions is one of the great mysteries of physics and is an instant Nobel prize for whoever figures it out! It's likely something to do with the interaction with quantum fluctuations but I'm out of my depth there.
Singularities break down any laws known to us as they are sealed off from the observable cosmos. It is hoped that one day Cosmology may answer this question, but it may take a long time.