I note that the snow camouflage pattern for T-34 tanks has sections where there is the green partially exposed with a "chain-link fence" patterns of white on those sections, rather than the whole tanks being covered with the white. What was that all about, and did all T-34's in winter 1941/42 have them or just certain ones?

White "rhomboid mesh" as a rule was to be brush-painted over secondary camouflage collors(brown or yellow) on Russian tanks.
Instructions for its application (Kolomiets,Moschanskiy-Tanks Camouflage in the Red Army 1930-1945) prohibited applying true vertical or horizontal strips of "rhomboid mesh", direction of "mesh" was to be at some angle to the ground.
The idea behind these strips was to mimic tyre imprints on snow covered roads, thus enabling to mask a tank standing/moving on road.