I'm not physicist, but let's get this rolling
1. The Big Bang occured before or after the existance of time?
We have no way of knowing at this time. Some say yes, some say no. Both string theory and quantum loop gravity imply not.
2. Did space-time BEGIN to exist?
Who knows?
3. Can changing/dynamic activity occur outside of the fabric of space-time?
Change as we understand is defined with respect to time, so not as we understand it.
4. If space-time began to exist at some point, why?
Who knows.
5. If changing/dynamic activity can not occur outside of space-time, how did space-time come to exist in the midst of the absence of space-time.
It is nonsensical to talk about space-time not existing "before" space-time since you're falling off the bottom of the time scale. If space-time has a beginning, then it exists at t=0, and there is no t<0 at.
6. What is inflation?
Inflation, as I understand it, is a period that occured during the very first fractions of a second of the big-bang during which the universe underwent an immensely swift expansion.
7. Since the fabric of space-time is expanding are my atoms stretching right now? Is my head getting bigger as I type along with everything in the universe? Or is the fabric expanding and leaving matter the way it is, and just creating more space?
No, no, yes.
8. If the fabric of space-time is expanding and matter is being stretched out with it, then how can there be room for any other fermions then the existing ones that took up all the space?
What fermions that took up all the space?
9. Can the spacial-fabric rip?
Dunno. It seems unlikely, it rather depends on whether the spacial-fabric is an actual thing. I believe the current favoured theories hold that it isn't, and thus cannot rip.
10. Because position can only exist in space time, can there be two spacetimes with no relative positions to each other, being in different realities of which we will never be able to reach?
We have no way of knowing at this time. Some scientists believe so.
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