Raman intensity, for that matter, the intensity of vibrational spectra, including IR and Raman, is the least understood area of vibrational spectroscopy. At this time, one can calculate and understand the intensity of Raman and IR spectra only for very small and simple molecules for which Schrödinger equation can be solved. Of course, there are abbreviated program in the marked that allows you to approximately calculate such information, but those are at best estimate.
Frequency shift of a certain Raman line depends on the purity of the material. For example, ZnO with perfect crystallinity and with some impurities, should be different because the packing of those molecules are different. The vibrational frequency is influenced by the intra and intermolecular force constant. When the packing of the molecules in the crystal changes, the intermolecular distance changes and thus the intermolecular force contents will change, resulting in frequency shift. If you want tp obtain detailed information, you need to know the symmetry of the molecule and perform very complex calculation called normal coordinate analysis.
Finally, full width at half maximum (FWHM) is a reflection of the structural distribution. Thus, for exactly the same molecule, crystalline material shows sharper Raman line than the amorphous material.
As explain by Dr Hatsuo Ishida, all spectra parameters are sensitive to the local or long range order of atoms in the compound. It is always a good practice to make relative measurements of these parameters, for example by comparison with a test-sample.
Some years ago we could rely some intensities changes to the presence of twins In other cases we explained the frequency shift changes du to strain effects in heterostructures and last the variation of FWHM to the change in the lifetime of the excitations involved in the processes.