in an electron-electron collision with a low speed and in the nonrelativistic case, approximately what fraction of electrons get significantly deflected (say more than 10 degrees)? Generally, with increasing the speed of the colliding electrons, does the number of not-deviated (reflected at 180 degrees) particles increase or decrease?
Nonrelativistic Møller scattering reduces to Rutherford scattering (plus exchange scattering) in the relative coordinate, and the Rutherford cross sections diverges for small deflection angles. All incoming particles are, to a greater or lesser extent, scattered. That means that it is not possible to talk quantitatively about the fraction of the total particles scattered through at lease some minimal angle, because there are an infinite number scattered by very small angles $\theta\gtrsim0$.