Why every galaxy is moving away from every other galaxy on astronomical scale? because of an explosion or because of creation of space? Why galaxies move away from each other in general on the astronomical scale?
Which answer is correct of the following?
It is because of the big bang theory, everything is just moving away from everything else on the astronomical scale, because of the explosion that happened in the past, just by inertia.
It is because space is being created all the time between galaxies, that is why they look receding from each other. Like drawing dots on a rubber sheet, then start stretching that rubber sheet. Dots are not moving, just more and more space is created between them.
Which answer is the right one? and if the 2nd answer is the right one, is it only space that is being created or spacetime?
 A: This is a little tricky, actually. You could say that the reason everything is moving away from everything else is the expansion of space. But you could also argue the reason we say space is expanding is that everything is moving away from everything else - after all, what does it mean for space to expand, other than that the distances between objects get larger?
We do have a perfectly clear mathematical description of cosmic expansion. It centers on the observational fact that the distance between any two objects at large enough scales (galaxy clusters and superclusters, not atoms or stars) is described by the equation
$$r(t_1) = \frac{a(t_1)}{a(t_2)}r(t_2)$$
The scale factor $a(\tau)$ changes in time in a way determined by cosmological equations, basically general relativity with some particular metric. (The FLRW metric is an artificial example.) This allows us to unambiguously determine how the distance between any two objects changes over time. But whether you interpret that change in distance as being a consequence of the expansion of space, or of space being created (though I really dislike that interpretation), or just actually being the expansion of space itself, is to some extent a matter of terminology.
Inertia is definitely not responsible, though. Inertia is a fine concept to apply when you're talking about small-scale objects, where you can ignore the effects of gravity; this allows you to have locally inertial reference frames in general relativity. But there are no globally inertial reference frames; informally, you can't continuously extend the concept of inertia on Earth's surface to, say, the surface of a neutron star, and certainly not throughout the universe.
Further reading: Why space expansion affects matter? and many other questions on cosmology on this site.
A: Can I recommend you watch Sir Roger Penrose lectures, Space-Time Geometry and a New Cosmology and Before the Big Bang.
And I also recommend you watch Prof Leonard Susskind lectures on Cosmology.
A: The correct way of thinking of this is that space is being created between the galaxies and that is why they seem to be receding from us.  Similarly, from any other galaxies point of view, we would also look like we are receding from them.
The current accelerated expansion of the universe makes this even clearer.  If the big bang were like an explosion, you would expect the fragments to be slowing down by their mutual gravity, but instead the dark energy is causing the expansion rate to increase, so it cannot be the explosion scenario.
The standard view is that the big bang singularity would have filled all of space at $13.7\pm0.2$ billion years ago. Since we currently don't understand how to handle singularities we can't really talk about that. However at any small time after the big bang the entire universe would have been filled with very high temperature and high energy density and space would have been expanding very rapidly. As time goes on the expansion rate would decrease until recently (the last few billion years) when it would have started to increase again due to the dark energy.
