Lets say that the space elevator works and one day it collapse what will be the results of that for a) asgardia and b) the rest of the world?

Depends on will it be a Earth space elevator or a lunar space elevator.

First it would be the reduction of launching costs, for both earth and Asgardia. Second, more people would have access to space, for many people are being cast off as unfit for spaceflight due to health problems. Those forces acting on a body inside of a rocket might cause health risks to people with fragile joints and other problems, where the Elevator makes the trip more pleasant.

I would hope that soon the Elevator will be functional as a reality. This is the only way my wife would join me in space. Perhaps one day this will be the stairway to Asgardia for those of us who are financially unable to afford space travel?

Legally, I'd figure that it would function similarly to a border does today, although I imagine that our laws regarding this "border" would be quite different than anywhere else.

Could someone explain the technical details