Yes, the lens is eligible for the extended warranty directly from Nikon.

You can switch between A and M via a small slide switch, just like with the 50 or 85 (both f/1.8). So it works. Does that help you?

Assuming you mean a Nikon Z APS-C camera: Yes, but due to the crop factor of 1.5, the 20 mm focal length becomes 30 mm, i.e. you cannot utilise the full wide angle. The advantage is that if you want to buy a Nikon Z full-frame camera later on, you can continue to use the lens and can then utilise the full wide angle accordingly. Hope that helps you.

Yes.