An attempt to answer your first question.

Cossacks were mainly Orthodox Christian.

Their history was often defined by their struggles against Catholic Poles, so that the hostile encounters between Cossacks and Poles wound up more deeply entrenching both respective faiths -- the Cossacks grew more fanatical in their Orthodox faith, the Polish grew more fanatical in their Catholicism.

Cossack encounters with Muslim steppe peoples also had a similar effect.

The Russian state was originally antagonistic towards the Cossacks, seeing them as rebellious outsiders. Some early Cossack communities were even formed as a result of Russian persecution, resulting in their fleeing out into the steppe and the foothills of the Caucasus mountains.

From the Encyclopedia of Russian History:

By the fifteenth century, the term was increasingly applied to a mixture of freemen and fugitives who had fled the serfdom of Poland-Lithuania and Muscovy to live in the seams between encroaching Slavic settlement and receding remnants of the Golden Horde.

However, as the Russian state began to expand in the 16th century, the presence of Christian peoples already residing nearby the lands into which they wished to expand was welcomed, especially as these communities were battle-hardened by the steppe lifestyle, making them perfect allies against the other peripheral groups Russia was presently sizing up.

Here's some books you may find interesting:

The Cossacks and Religion in Early Modern Ukraine

This above book is the most relevant to your interests. The remaining below only peripherally relate; though I learned a great deal from each on the topic.

Dagestan: Russian Hegemony and Islamic Resistance in the North Caucasus

Russia and the Golden Horde: The Mongol Impact on Medieval Russian History

Empires Apart: A History of American and Russian Imperialism

This last is fascinating, describing how, just as America was conquering its West from the Native Americans, Russia (primarily led by Cossacks) was pushing into its East, eventually conquering Siberia, which was the prize of the Cossack victories.

For more on this last topic, should you be interested, check out the chapter titled "The Parallel Russia / USA and the Ideological Construction of Geographical Space" in the book Euro-orientalism: Liberal Ideology and the Image of Russia in France (c. 1740-1880)