1.) We teach a lot of very handwavy material in introductory general chemistry at the university level here in the US. It does not mean that such material never gets a proper treatment. One thing to keep in mind is that such a course is generally intended to appeal to a wide audience, frequently to no one's complete satisfaction. (Especially the premeds.)
2.) Who the frak wrote this Wikipedia entry? I emphasize the following:
Nitrogen-15 is frequently used in nuclear magnetic resonance spectroscopy (NMR), because unlike the more abundant splinless nitrogen-14, it has a fractional nuclear spin of one-half, which makes it observable by NMR.
Just so we are all clear - you can do 14N NMR. See, for example, the excellent webpage here for a bunch of references on exactly that. It's just that 14N is a quadrupolar nucleus (I = 1), which makes life a little more interesting, but is not everyone's cup of tea.
3.) Inverse problems can be challenging. Obviously.
And with that, I'm done. At least until next time!