How do I get high production to build wonders?

I've never gone this route, with Cultural victory as the end goal, but am curious to try. Key question: do World Wonders always stay in tact when you capture cities? What about great works?

World Wonders always stay intact when you capture a city.

National Wonders are always destroyed.

As for Great Works, they will stay intact if there was still spots they could be housed in after some of the buildings were burned.
 
If any GWs are stored in a national wonder or in a building that happens to be destroyed when the city is captured, the affected GWs are automatically moved to open slots in other buildings or wonders in that city or in other cities that you control (whether annexed or puppeted -- Note: if you are razing any cities at that time, check to make sure that no GWs were moved to those cities -- if so, move them manually to another city or pause the razing process). If you don't have enough open slots in that city or in other cities, the excess GWs will be deleted and removed from the game.
 
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