I tried out the 35mm 1.8g and 18-55mm kit lenses (both DX lenses) on my F4. The Lenses will work with the two program modes and if I recall the shutter mode. The 35mm needs to be shot pretty well wide open to prevent the corners of the frame darkening. So I used the hi program mode. (It attempts to use higher shutter speeds so it is more likely to keep the lens wide open. The 18-55mm is totally usable zoomed in past about 22mm.
Here's a few photos shot with those two lenses on the F4: