To become an instructor for NRA Basic Pistol (or rifle, or shotgun, or any other NRA discipline), you must first take the NRA Basic Instructor Training (BIT). This can only be taught by NRA Training Counselors. You can visit NRA's website, under education and training, to find such courses near you.
After BIT, then you choose which discipline(s) you wish to become an instructor in. Again, only a training counselor can teach these.
NRA Basic Pistol does satisfy requirements for a carry permit in some states, but I wouldn't go so far as to say most (by definition, more than half). It varies by state (FL will accept any firearm training course, not just pistol).
Basic Pistol only teaches safe gun handling and basic marksmanship; it does NOT teach defensive or tactical shooting, nor does it go over legal consequences. These also vary by state. I caution anyone I know who carries, whose formal training is limited to a basic pistol course.
I'm not afraid of the guy who wants many guns; I'm afraid of the guy who wants just one.