Diffraction is the bending of light round the edges of an obstacle or slit into the region of shadow. It is most noticeable when the slit width is of the same order as the wavelength. A single slit gives a wide central bright band with weaker bands on each side.
A diffraction grating has thousands of equally spaced lines. It gives sharp maxima at angles that depend on wavelength, so it is used to measure wavelength. The planes of atoms in a crystal act as a grating for X-rays, whose wavelength is about the same as the spacing of the planes.
Polarization limits the vibrations of light to one plane. Only transverse waves can be polarized, so this proves light is transverse. Sound, being longitudinal, cannot be polarized.