Nintendo NES Controller
Yes they are.
No this is for an 80s nes console
No, this is for the original 1985 system. You're looking for the "NES Classic controller.". Gamestop sells them for about $17. Alternatively, you can use a Wii classic controller I'd you can find one. They are usually cheaper.
Depends on what they have. Most of their stock is real NES controllers, but a couple knock-offs might slip in. Be careful.
Yes, this is an official Nintendo controller for the original console, not the NES Classic pre-game installed console. Help that helps!
It only works with the original Nintendo from 1985 or the systems that play NES games like the retron