I do not want to break any nyc code law.
Non-metallic (NM) wire also known as Romex(brand name) is used in residential wiring but must be installed according to the National Electric Code (NEC). As it says in the first section of the NEC, All codes are subject to the authority having jurisdiction Which means your local electrical inspector has the final say. Your best bet would be to call your local inspector and ask him or her if you can use NM in your application.
Non metallic tubing as it is referred to is a protective layer for conductors. Legal depends on what you intend to do w/ it and what your local and state jurisdictions say is legal. It is generally used in wooden structures, like homes but only when the wire is subject to damage by human traffic. A green/bare ground is required in most cases to ground the appliance since the tubing is plastic. Most commonly seen used outdoors because of it non corrosive qualities and aesthetic appearance
like what ? carbon fiber ? I don't know of any non metallic wire