If the universe contracts and gets smaller could a civiliation move outside of it?

There is no outside.  The universe is spacetime.  Same thing.  Spacetime is created by gravity which is generated by mass.  The universe grows when mass moves out.

Fundamental physical laws say that you don't get to move outside the universe until you are completely civiliated.

Yes provided you can find the door to the outside area. Knock on the walls until you hear a hollow area.

No. There is no outside to the universe. 

No.  Look up the definition of 'universe' and see if an outside exists anywhere.

The Universe is NOT contracting. It is expanding and he rate of expansion is accelerating. Your premise is false and your factsare false and uncoordinated. 

There is no "outside" to the universe.