Infinite universe? How? So it seems the overall thought is that the universe is infinite. I don't get how.

Most depictions I read mention something to the effect of "at 1^-20 seconds the universe was the size of _". (Essentially mentioning a finite size at a very small length of time). So it came from a singularity, and had a finite size at some point. No matter how fast inflation went, any multiple of that finite size is NOT infinity though. If it was finite once, it is still finite.

If it's infinite then it was always infinite which means it was infinite density, infinitely large, etc. That's too crazy to swallow.

Isn't it more likely that the universe is really really big but not infinite? And we are at the center of the observable universe (to us), however we are off center in some grander universe that's maybe 1 trillion light years across? And nothing is past that because space and time are the same thing. Therefore if there is no light/matter/events, there is no time and hence no space.
Depending on the mass of the universe, the universe has three different possible shapes.
http://en.wikipedia.org/wiki/Shape_of_the_universe

It can be finite or infinite depending on the shape it has, and there are some ways we can discard possible shapes (if it started to shrink instead of expand).

Hope this helps