The Schwarzschild radius of the observable universe is 10 billion light years. Me thinks that for the mass to be compacted into a smaller space at some point in the past, it would have either had to escape it's own event horizon (since under most current definitions it would be a black hole), or the definition of light-year had to have changed from what it is today. In that regard, the only thing making up the definition of light-year is distance and time; so space-time itself was radically different way back then (from our current perspective of relatively low energy densities).
Both! If the universe is flat, then it was always infinitely big. And, according to the inflationary universe theory, it expanded faster than the speed of light too.
In this case, you have to think of "expanding" as being like stretching. I.e., things within the infinitely big universe rapidly got farther apart from each other.
Everything we can see (which is called our "Hubble sphere") started off as a tiny little (and very massive) speck of stuff at the beginning of time. There were infinitely many tiny little specks, and they all became different Hubble spheres. But all the Hubble spheres all overlap each other, forming one continuous space. The same thing was true about the little massive specks at the Big Bang.
As I said above, at the time of the Big Bang, the universe was like a very dense sheet of rubber, and then it started rapidly stretching, getting less and less dense over time, until it is now the density that we see around us.
Infinities can definitely give you a headache, though. For instance, there are just as many odd integers as there are integers.
