What was the extent of cooperation?

From c. 1926 onwards, German officers and pilots were sent to train in the Soviet Union, and tank designs were built and tested there as well, like the Grosstraktor series.

How much sharing of strategic and tactical insights was there?

How much did one influence the other's developments through the '30s? How much can we say was essential, even?

What effect did this cooperation have on the combat of 1941 onwards? Did it assist the preparation of any one side?

The book Storm of Steel: The Development of Armor Doctrine in Germany and the Soviet Union, 1919-1939 by Mary Habeck is an excellent source for this. In short, there doesn't seem to have been considerable sharing of ideas. While there was some minor influence on German and Soviet developments from outside, both developed largely organically and parallel to one another.

Although Soviet armoured developments were derailed by the Purges, by 1941 Mechanized Corps and ultimately Tank Corps were being reintroduced. Whereas Soviet Industry and ultimately Western Allied Lend-Lease aid would enable for a highly mechanized/motorized Red Army by 1943-44 (although use was still made of horse transport), integration with infantry and infantry-armour cooperation was an issue that would plague German developments for pretty much the whole war, with mechanized/motorized elements being concentrated in the Panzer/Motorized Infantry/Panzergrenadier forces, and the majority of the Army (infantry & artillery) still being heavily dependent on horse transport.