In my experience looking at the source code of programs written in a different language is rarely helpful. It's only useful to glean some general ideas or algorithms. But rewriting with one eye on some C code? Rarely helpful and usually counterproductive.
Not necessarily. The non-GPL utilities the GNU coreutils are based on are presumably licensed as MIT, ISC, Public Domain, or similar. If that is the case, those licensing regimes don't forbid adding extra restrictions, so adding the restrictions of GPL would be permitted, and the new derived (again, assuming interfaces are copyrightable) work would operate as being essentially GPL licensed. Things get murky as there are proprietary utilities too that coreutils are probably based on, but then there are also specifications of behavior (SUS, Posix) which might or might not sever the "derivation path" of the work, or might introduce further licensing constraints.
Do you view APIs as something other than an interface? A ruling from the Supreme Court may not reach the ultimate issue, but if it does, what assumptions would you make concerning the difference between an API and a program’s interface with the user?