Yes, it will fit Nikon FX cameras, but the camera will automatically switch to 'DX Crop Mode,' resulting in a lower resolution image to avoid heavy vignetting.
It is best suited for outdoor daylight. While the VR II stabilization helps with slow shutter speeds, the f/4.5-5.6 aperture is not ideal for very dark environments without a tripod.
Yes, the AF-S designation means it has a Silent Wave Motor (SWM), allowing it to autofocus on all Nikon DX DSLRs, including entry-level models like the D3500 and D5600.
No, it is not waterproof. It features a weather-sealed rubber gasket at the mount to resist dust and moisture, but it should not be used in heavy rain without protection.