In relation to the first question, the one concerning divine right, Catherine's reign showed how the ideas of the Enlightenment could be reconciled with autocratic rule. Catherine was very much a devotee of the radical new ideas sweeping across Europe; but at the same time, she was an autocrat, and took her role as Empress very seriously. Catherine wasn't about to give up the enormous power she'd inherited, no matter how much she admired Voltaire.

Though Catherine was relatively tolerant in matters of religion for someone of her time—especially for a monarch—she was nonetheless canny enough to realize the immense political value of her subjects believing that she'd been divinely ordained by God to sit upon the Russian throne. For Catherine, religion was primarily a useful means of social and political control, and a way of bringing order and stability to her massive multi-ethnic empire. Such a utilitarian understanding of religion was entirely consistent with Enlightenment rationality. The Empress may not have believed in the divine right of monarchs, but she certainly believed that she was entitled to wield absolute power. In that sense, one could interpret Catherine's autocracy as an example of secular absolutism, albeit underpinned and reinforced by religious tradition.

Catherine the Great (1729-1796, also known as Catherine II)  was actually a German princess who was betrothed to the future czar of Russia, Peter III.  Although originally Protestant, she converted the Russian Orthodox Church, learned the Russian language, and ingratiated herself to the reigning monarch Elizabeth I. After Catherine's husband died "in an accident," she became the ruler of Russia, and it expanded its influence south into the Ottoman Empire after winning the Russo-Turkish War, and west into Poland, eventually partitioning that country. She is credited for starting the "Russian Enlightenment,"  and overhauled the Russian legal system to include equal protection under the law for everyone, at a time when the class structure of the culture was still in place. By beleiving she had the right to rule Russia, it could be understood that she adhered to the Divine Right of Kings (or in this case, Queens) and was an Absolute Monarch, but in practice, by moderinzing Russia's legal and educational system and her other reforms, she could be considered more of an Enlightened Despot.