What were non-Muslim religious communities within the Ottoman Empire called?

Answer 1

Millets.

Non-Muslims who lived in the Ottoman Empire were called Dhimmi, or second-class citizens. They lacked a number of fundamental rights such as freedom of movement, freedom of settlement, access to all occupations, and additional taxation because they were Non-Muslim. Each Dhimmi group, like the Armenians, Greeks, Jews, and so forth were organized into Millets which were community representative groups. Each Millet would report to a centralized Millet representative in Istanbul who would have direct dealing with the Imperial Palace. This would allow the Millets to air their grievances, but was more often used as a method to control the Millets and make them less resistive to Ottoman Occupation.