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here.
AFAIK villages provide grain and part of province gold income, so if you control only a city, it would starve when food reserves ran out. Because of the same reasons an attacking army needs supply wagons or they would start to starve almost immediately after crossing the border.
To stop rebellions, garrison more troops there, but remember they would need something to eat too (in an occupied city, army takes all the food it needs first and citizens have what's left, if there is nothing left they will revolt or escape to other cities).
Also keep in mind than unlike most strategy games where you can safely absorb minor independent cities, here you'll face a war against your powerful neighbors soon after you begin your aggressive world conquest, so careful planning is a neccessity.