Civilization – Why can’t I build the Sydney Opera House in Civ5

Although bwarner's answer was helpful as always, no one verified beyond "I think so" that puppet cities are affected by each of the civilization wide effects, so I did some testing and:

Yes, puppet cities are affected normally by all civilization-wide effects.

I can't verify that there are no exceptions, but I verified at least one of each of the things I was concerned about...

The Testing

Civilization Special Trait

I loaded up France on easy, and went about conquering. Japan fell, giving me Kyoto to play with. As soon as I conquered the city and took it as a puppet, it was producing 2 culture. This matches perfectly with France's ability, so CHECK!

More Test Setup

Having acquired my victim, I setup the test: social policy ready, golden-age ready, and wonder ready all on the same turn! (Save file available upon request, whenever I get around to it after that.)

Before

Social Policy

I enacted Liberty->Republic, which gives +1 production/city. That matches, so CHECK!

Golden Age

I already had culture working for me, so I started the golden age by enacting the social policy Piety->Reformation. Clearly shows an increase in both gold and production, CHECK!

World Wonder

If you take a look at all of my cities from the same turn, you can see Orleans is about to finish the Sistine Chapel, which gives +33% culture/city. I went to the next turn, and without any growth or buildings completing, the after shows increased culture on Kyoto. (Lyon also started with 7 culture and ended with 9 as well, so the rounding definitely matches.) CHECK!

Everything checks out. I suppose puppets really are just normal cities that you don't control. I would still love to hear if anyone finds any exceptions!

The amount of production of a great engineer on normal speed is calculated using the formula

300 + 30 * city population

So in a city with a population of 1 the engineer only results in 330 production, in a size 15 it results in 750 production.

For quick speed the formula is:

200 + 20 * city population

For epic speed it is:

450 + 45 * city population

and for marathon it is:

900 + 90 * city population

The amount of hammers does not seem to be influenced by era, map size or difficulty level.

Conclusion: If you want to hurry late game wonders, build it in a city with a large population.