The principle is the same as for radiative surface cooling during a long night with clear sky. Just in larger spatial and temporal proportions.
Is it also because of the lack of daylight too ?
Longer nights and little daylight lead to more intensive radiative cooling. Snow cover helps, as while snow reflects visible light well, it is like a radiating black body in the thermal IR region.
Considering that Siberia lies in the eastern region of Russia and because the wind generally blows towards east, it'd get colder the further east you go. Does that add any effect to Siberian High too?
There is no direct relation. Mostly western winds in Europe are caused by controling Atlantic low near Iceland and the high near Azore islands. Siberia and Central Asia have continental climate with big summer/winter temperature difference, as tempering ocean effect is minimal.
The pressure high formed by cold and dense air causes counter-clockwise outward winds around itself.
That cold air is stable, as surface is even colder. If it came over warmer surface, it would cause an intense cold front.