Question on Field of View of DX Lens on my D7000

I have a Nikon 35 mm f/1.8 prime DX lens. Does the DX mean that the field of view, when the lens is used on my D7000, is actually equivalent to what an FX 35 mm lens would be on an FX camera or does the "1.5 X crop factor" apply giving it effectively a field of view equivalent to a 52 mm lens on a full frame camera?

So in terms of field of view, does my 35 mm DX on my D7000 become like my 50 mm was on my old Nikon film camera?

Finally then, if I wanted to obtain a field of view on my D7000 equivalent to that of a 35 mm lens on full frame camera, would I need to use a 24 mm lens?