I own a N8008, which is known as F801 outside of the USA. Lens compatibility is the same as N8008s/F801s.
I don't own the lens in question (AF-S 35mm f/1.8G DX), but I do own other AF-S G lenses.
AF-S G lenses will mount and meter on the F801s.
It will not auto focus, but you can focus manually.
It will work as expected in S and P modes, where the camera body selects the aperture.
In M and A modes, you cannot select the aperture. The lens will be fixed at the smallest aperture. The meter will work just fine, but you will always be at f/22. Perfectly usable in bright light, with a strong flash, or non moving subjects and a tripod.
With the 35mm DX lens, there will be some vignetting (slight darkening of the corners), but surprisingly this particular lens has almost full coverage of the 35mm frame. Some DX lenses are OK on 35mm, others are not.