How did the Ottoman and Safavid Empires treat the religious minorities they conquered? Also, what is the Ottoman Janissary system and the rivalry...

Like many empires throughout history, the Ottoman Empire conquered many people and sought to convert them to their own religion. Those that did not convert were given second-class status, called zimmis, granted some limited autonomy but still subject to Ottoman rule and Islamic law. This was better than religious minorities were treated in many other parts of the world, but hardly equality.

The Ottoman Sultan Marad I formed the Janissary from captured Christians who were pressed into service as a personal bodyguard for the Sultan. His successor, Marad II, expanded their role to be an elite military corps that served a variety of functions---but still maintained the general practice of pressing Christians into service. Eventually they became a powerful interest group in their own right. In a time when most armies were gathered ad hoc from serfs and peasants, the Janissary formed something much closer to a modern standing army. They used firearms, which at the time were state-of-the-art.

The Sunni/Shi'a conflict has been a part of Islam since a generation after the religion's founding, so it's hardly limited to the Savafid Empire; but it was certainly important there. Though Shah Ismail was originally Sufi, he converted to Shi'a, and declared the independence of the Savafid Empire from the Ottoman Empire when the Ottomans outlawed Shi'a and mandated Sunni Islam.

Ismail then made the Savafid Empire a Shi'a state, despite the fact that most of the population was in fact Sunni. This led to a campaign to convert the population to Shi'a, ranging from propaganda to outright coercion. This conversion of the population to Shi'a was largely successful, and to this day Iran is a Shi'a state with a predominantly Shi'a population.