The Big Bang occured before or after the existance of time?
Let's look at it this way.
Take a sphere:
This sphere has two coordinates:
"North-South" and "East-West".
However I could describe position on the sphere with any set of two coordinates.
"North-South" and "East-West" are just the most suitable or "the easiest".
The fact that you need to use two coordinates make a sphere a 2-manifold.
Spacetime is a 4-manifold, so we need four coordinates to describe position in it.
Sometimes the most suitable are "t", "up-down", "left-right" and "back-foward".
When we are measuring distance in a part of spacetime we use the following formula:
(total distance squared) =
- (distance in coordinate 1 squared)
+ (distance in coordinate 2 squared)
+ (distance in coordinate 3 squared)
+ (distance in coordinate 4 squared).
As you can see, the first coordinate has a minus sign in front of it.
The coordinate with the minus sign in front of it is what you will call time in that part of spacetime.
Most of the time the coordinate with the minus sign is "t".
So we will call lower values of "t" the past and larger values of "t" the future.
However sometimes another coordinate will get the minus sign, so for instance if "Up-Down" got the minus sign where you are, you would call "Up-Down" time.
So "down" would be your past and "up" would be your future.
In this way, what is time and what is the past and future depends on where you are.
An example of this is how you fall into a black hole.
You don't fall into the Black Hole because you are pulled in, but because the Black Hole warps local spacetime, so that the inside of the hole becomes your future.
So you "exist" into the hole, away from the hole becomes your past.
The Big Bang is just a point in spacetime.
This point didn't happen before time began, because time is just some direction in spacetime, and what that direction is depends on where in spacetime you are.
Did space-time BEGIN to exist?
In General Relativity "begin" means the furthest point into the past of an object.
However this only applies to objects in spacetime, words like "past" and "future" are only directions inside spacetime and mean nothing to it itself.
Can changing/dynamic activity occur outside of the fabric of space-time?
Possibly, but not in a "before-after" way if you get what I mean.
What is inflation?
Think of the Universe as the Earth.
Each Longtitude up from the south pole to the North pole is the Universe at a given time.
The South Pole is the Big Bang for Example and the North Pole is the Big Crunch.
Each Circle is the Universe at a different time.
The Universe at a given time (Each circle) gets bigger away from the South Pole.
To us this looks like Inflation because we crawl up each bit of longtitude and see the circle getting bigger.
In reality the Universe was always been this shape and is static.
The Circle seen here would be the Universe at its maximum size, half way between the Big Crunch and Big Bang.
As you can see, whether there is space outside the Earth or not doesn't matter when discussing this.
A similar case applies to the Universe.
(I know there doesn't necessarily have to be a Big Crunch, but this is just to make the Example simpler.)
9. Can the spacial-fabric rip?
Theories of Quantum Gravity and String Theory say "Yes".
However these haven't been verified so I'd just say maybe.
(Even though personally I'd say yes)
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?
Yes.