Look at the table of wavelengths of the electromagnetic spectrum here. X- rays are of the order of keV , wavelength of nanometers. Atomic spectra, i.e. electrons falling back down to an empty orbital are of the order of keV. Visible light used for double slit experiments is of order of eV, wavelength microns of meter. This answers the question of the slits, the slits have to be of order of microns, and x-rays would just pass through without interacting in the scattering "photon scattering off two slits of ~micron size and ~micron distance apart"
Here is a simple description of how X-rays work in amorphous material, as the human body:
They can, however, knock an electron away from an atom altogether. Some of the energy from the X-ray photon works to separate the electron from the atom, and the rest sends the electron flying through space. A larger atom is more likely to absorb an X-ray photon in this way, because larger atoms have greater energy differences between orbitals -- the energy level more closely matches the energy of the photon. Smaller atoms, where the electron orbitals are separated by relatively low jumps in energy, are less likely to absorb X-ray photons.
The soft tissue in your body is composed of smaller atoms, and so does not absorb X-ray photons particularly well. The calcium atoms that make up your bones are much larger, so they are better at absorbing X-ray photons.
There exists though x-ray crystallography where diffraction can be built up by the coherent scattering of X-rays from an ordered body, similar to the pattern of double slit.
X-ray crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline structure cause a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.
So the possibility of building a diffraction pattern is utilized in ordered materials. In the disordered ones one only gets the shadows of the absorption during the incoherent scattering of X-rays with the atoms of the material
Last question why is light diffracted by the electron cloud but not the atom's nucleus
The incoherent absorption of Xrays happens because of the energy levels of the electron orbitals which allow the transitions of the electron, these are of the wavelengths of Xrays. In coherent crystallography again , the wavelength of the X-rays are of the order of the interatomic distances, whereas the probability of an x-ray of that wavelength to hit a nucleus of much smaller wavelength is much lower. It is with gamma rays whose wavelength is of the order of the nuclear size, ~picometer, and energy in ~MeV that the probability of interaction with a nucleus is large.