When I go to city view mode none of the new conquests wonders are shown. There is a big "flattened" space that looks like an invisible building is there or something, but the wonders are never shown. Older wonders are fine, just the [c3c] ones aren't shown. How do I fix this?

Sorry, this is not fixable. This was Conquests' intention.

Due to lack of time, Firaxis made a choice of gameplay over artwork and rarely used features. The new C3C wonders and improvements don't show in the City View, nor does City View even appear in scenarios/mods. You can still see older wonders/improvements though.

In addition to me not being able to see the new conquests wonders, I am also not able to see the Sistine Chapel for some reason. Should this be happening?

As I said in the other thread, joelgf, it sounds like you are missing files - try a reinstall.