Is NA the same everywhere?

basically, yes. In detail: some doctors are using thicker needles which might increase the danger of damage.

Is there a difference between US and France? Most doctors in the US learned NA in Paris. Dr. Lermusiaux probbably has the most years of experience, being one of the "inventors" of NA. But in the mean time doctors like Charles Eaton, who started NA in the US, and Keith Denkler have lots of experience, too.

Is the cord cut completely? The normal process is to weaken the cord by stitching it with a needle and then tearing&breaking it mechanically. Sometimes that doesn't work out and the cord is just elongated to achieve a straight finger. That will likely result in earlier recurrence. But usually the cord is broken completely.

Wolfgang

NA can "cut" through the cord or is can be used to just weaken the top layers and then the cord can be manually snapped.
NA tends to break up the cord into multiple segments, rather than "lengthening" the cord.