Without getting into too much detail:
No, it's boundary is just a side effect of the definition. We use zero value to be the boundary, but that's just a convenient convention.
NURBS and other parametric surfaces still have limitations. It's very difficult to define complex shapes with them, and the boolean operations often break, leaving you with gaps between patches or surfaces that have no matching other side. The staff and beta testers include people experienced with polygon and NURBS, and there are things people are used to not being able to do (or have to do certain ways) with NURBS that "just work" with this system.
Functional objects aren't new, by any means (they predate polygons in fact). We're using some new functions (rather then the boolean ones used in existing CSG modelers).
3D printing resolution IS limited by the polygons. If you try to put a mesh into any existing printing software that has individual polygons sized at the precision of the motors, the software does break (and the mesh file will be measured in gigabytes).
And yes, "resolution of nature" is a marketing phrase. Don't ask me, I just work here.
Disclaimer: I work for Uformia, the company running the Kickstarter. We have an existing product (which isn't mention in the summary, but is in the Kickstarter) but we want to make a more specific user friendly version.