In the beginning they were tolerant, in order to appease the populace, while assimilating or eliminating the ruling aristocracy (which is typical of all conquests). That means that they took care to affirm some priviledges of the upper classes and clergy, creating incentives for people to convert, and killing off possible troublemakers. Several churches were spared and not converted into mosques. After they had firmly established their rule in the new Balkan territories, they became more brutal and repressive (around the 15th, 16th and 17th century). With the decline of the Empire in the 18th and 19th century the situation for the Christian subjects became better, both because the central governement lacked the power to effectively oppress them, and because European states intervened, for their own purposes, to "protect" various Christian ethnic groups of the Empire. But that didn't mean that life under a peripheral warlord Pasha in his semi-autonomous region would automatically be better than under the Ottomans.

There were many rebellions throughout the history of the Empire, large and small ones. It would be pointless to number them all here. I can't judge about the relative level of Ottoman brutality, esp. when I think about what the Spaniards and English of the period liked to do, but apparently, the suppression was, more often than not, violent.

Gregory Palamas was captured and held hostage by the Turks in 1355, and saw how Christians lived in the newly conquered territories. According to D. Nicol, he was at times pleasantly surprised by the tolerance the Turks showed towards their Christian subjects. Which could possibly have been Ottoman propaganda or realpolitik. Others noticed how in the conquered territories everything had declined, wilderness had taken over the villages, and even the names of towns had been forgotten. (I can't remember the exact quotation). And the more the Turks advanced, the less they were willing to show a good face to the conquered peoples. After the conquest of Constantinople, stories about the mistreatment and oppression of Christian subjects abound. Many Greeks and Christian Albanians at the time fled to Italy, Sicily and Corsica.

IMO, the basic problem with the Ottoman-Christian relationship was that it was based on "privileges", not established and unalienable rights. According to islamic law, even the rather tolerant Hanafi school of the Ottomans, Christians were Dhimmis, and therefore had, by definition, an inferior legal and social status than muslims. Any privileges granted by a sultan to a class, profession or region with a firman could and often would be revoked by his successor. Churches that were granted immunity were eventually converted in to mosques, trade, tax and military privileges given to a village, town or region were revoked, suspended or expanded, according to the whim of the ruler or his Vizier - resulting in a centuries-long haggling and bargaining between the Muslim rulers and their Christian subjects.

Were the Ottomans particularly violent in suppressing rebellion?

Pretty much yeah. But is not limited to Christian rebels really. For example, when the House of Saud rebelled (the very same ruling house of Saudi Arabia today) the Ottoman sultan sent his army from Egypt to Arabia to destroy the rebellion. The army captured its leader, sent him to Constantinople, and the sultan had him beheaded.

The same fate also befell Ali Pasha of Ionina, the Albanian warlord who ruled de facto state in Southern Albania and Epirus (Greece), he was also beheaded by the order of the Sultan.