Question about wonders/domination

If I conquer a city, do I obtain the wonders that were built in that city? Do they apply? If I raze the city can I possibly rebuild wonders that that particular civ got?

Yes, you get all wonders (but no national) and their long term traits, like bonus culture, gold, food, science still apply, as well as any special abilities. At the same time you don't get any units that have been given to the civ built a wonder.

Each wonder can be built just once and you loses it forever if you razes the city it is built in.

Are effects from wonders watered down in Puppet cities? Is there any benefit to annexing a captured city with wonders?