How/why did the Thomson scattering by early plasma of the CMB create a particular polarization? I understand how Thomson scattering polarizes EM radiation, but why/how did particles of the early universe create a particular polarization pattern of the CMB? (E-mode polarization)....
I mean, the scattering particles were moving/scattering/oscillating in all different directions, so why a particular polarization pattern?
 A: The polarisation of the CMB refers to the extent to which the electric field of the radiation received from a particular direction oscillates in one particular orientation, rather than having a random  orientation in the plane perpendicular to the wave motion.
Polarization of the CMB is caused by Thomson scattering from free electrons just before they combine with protons and the Universe becomes transparent to the CMB radiation.
The polarization occurs because the radiation field seen by the electrons is slightly anisotropic, it varies according to which direction the radiation is coming from because of small temperature and density inhomogeneities caused by acoustic oscillations. In particular, polarisation requires a quadrupole anisotropy of the radiation field and these can be produced on length scales equivalent to how far photons can diffuse just before recombination, corresponding to angular scales of around 0.002 degrees in the present day CMB. These anisotropies are the fingerprints of what went on in the early universe and depend on what the values of the cosmological parameters are.
There is an excellent primer on this topic - http://background.uchicago.edu/~whu/intermediate/polar.html
