Hi Tom
Actually, the cossacks really started to exist after the battle of Kazhan. The cossacks were people, mostly of Russian origin, who were allowed to populate the frontier regions gained during the Russian expansion starting with the reign of Ivan the Terrible. So, no participation at Kazhan and maybe Anecdotic at Orsha.
Cossack culture is quite interesting. They lived a semi liberated life - little or no taxes, had a kind of tribal democracy with the election of their chief - the Ataman. They were known to be thiefish ruffians with fierce spirit of independence. The Zar used them to secure frontier regions with far away regions just as the Caucasus - Terek cossacks, the southern uUkraine - Don and Zaparoshni cossacks and Siberia - Ural cossacks. They would aquire a lot if the cultural traits and also warfare from the frontier tribesmen they were asked to dominate.
Cossacks fought the Tartars and the Turks, and they fought the big uprising after the Poles had annexed most of Ukraine (after Battle of Orsha).
There is some good reading:
Zinkievic « with fire and iron » about cossack uprising
Tolstoi « the cossacks » about life of Terek cossacks fighting the Tchetchens
« The quite Don » official author is not the real one describing the doom of the cossacks after 1st world war and during the Russian revolution.
Another very good one is « Taras Bulba » by Nicolai Gogol, cossacks fighting Polish
Good reading
Michael