Next: What do you propose is going through the double slit experiment here? The gravitational wave? Matter is transparent to gravitational waves, so it would be difficult to build such a double slit experiment. As another poster here mused, you could probably make some kind of interesting meta-material analogous to a crystal lattice and get some interesting gravitational-wave diffraction pattern. But I'm not sure if this is what you're getting at. The point of the famous double slit experiment for photons is that it shows the dual wave/particle nature of photons (or other elementary particles like electrons). Since we don't have a quantum theory of gravity I suppose it's an open question what the outcome of such an experiment with gravitational waves would be.