Did the Ottoman Empire allowed non-Muslims to practice their own religion if they paid a special tax?

Answer 1

Generally speaking, YES, although this deserves to be clarified.

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.

Admittedly, life under the Ottomans was far superior to most contemporaneous Empires. Spain was by far a more religiously and culturally intolerant place during this period as were France and England.

Finally, the Ottomans' most egregious crime was the policy of devşirme, where Christian families in the Balkans region had to submit to Ottoman soldiers stealing their children to bring to them to Istanbul where they would have no contact with their parents for years and be trained to be the elite Janissary Core and be converted to Islam. No Muslim was even allowed to join the Janissaries, because the devşirme system was so effective in producing recruits loyal only to the Emperor because they feared him.