Does the Cosmic microwave background (CMB) have an amplitude? Does it vary, like the 'temperature' (wavel./freq.) and the polarization?

The fluctuations are accenuated in the ubiquitous plots that you see of the microwave sky. For example this image constructed with data from the ESA Planck satellite. The temperature fluctuations in the intrinsic CMB are at the level of about $$\pm 0.0005$$ K compared to the mean temperature of 2.73 K (i.e. 1 about 2 parts in $$10^5$$) so are exaggerated in such plots. The amplitude variations (as a percentage) are a few times bigger. These anisotropies are caused by variation in the plasma conditions at the time of recombination.