for corruption, theres a number of ways to reduce it. the most obvious is to build structures like police stations and courthouses. another way, is to build the forbidden palace away from your capital near the cities where corruption is the highest. lastly, if u have 30 cities or less, switch to democracy. if u have more, use communism.
for civil disorders, give them entertainers, even if it means a food shortage. make sure the number of unhappy citizens are less than the number of happy people, ALWAYS. to do this, try to get as many luxuries as possible. or increase the "happiness tax." If you are at war for a long time, your people might be experiencing war weariness, so u might have to give them some peace.
as for destroying cities u don't want. use the city to make workers/settlers until it reaches a population of 1. try to make another worker, and it'll ask u if you want to abandon the city.
civ3 is a frustrating game for the beginners, but be patient and it pays off. have fun.
Dan