Understanding the structure of NCS⁻
This is a misprint. Here is a similar problem (OpenStax Chemistry, retrieved from https://opentextbc.ca/chemistry/chapter/7-4-formal-charges-and-resonance/) that makes sense and has a correct answer:


  As another example, the thiocyanate ion, an ion formed from a carbon atom, a nitrogen atom, and a sulfur atom, could have three different molecular structures: CNS–, NCS–, or CSN–. The formal charges present in each of these molecular structures can help us pick the most likely arrangement of atoms. Possible Lewis structures and the formal charges for each of the three possible structures for the thiocyanate ion are shown here:
  
  
  
  Note that the sum of the formal charges in each case is equal to the charge of the ion (–1). However, the first arrangement of atoms is preferred because it has the lowest number of atoms with nonzero formal charges (Guideline 2). Also, it places the least electronegative atom in the center, and the negative charge on the more electronegative element (Guideline 4).


The statement made rationalizing the incorrect structure is also flawed:


  "is more stable because each atom has non-zero formal charge in the lowest energy state"


This is an ion. Some atom has to have a non-zero formal charge because the net charge should equal the sum of formal charges. Why having each atom have a non-zero formal charge should result in a more stable structure is not clear to me. Mentioning the lowest energy state is curious as well. Maybe they meant most relevant resonance structure.

One should also keep in mind that formal charges are mostly an accounting method and do not reflect actual charge distribution (see https://chemistry.stackexchange.com/a/119771).