Ok, questions about this:

How does it work, exactly? What are the rules in regards to capturing enemy cities or city-states? Do puppeted or annexed cities break the OCC (at least, achivement wise)? Am i stuck only trying for a cultural, diplomatic or space victory?

If you click on "One City Challenge" in the advanced settings, you will only be able to found one city. Settlers will not be able to be trained. When you capture an enemy city (even it's capital) you won't receive money for looting it and you won't have an option to raze, puppet or annex, it will just instantly disappear. You also can't liberate city states, they will just disappear. Remember that the AI isn't affected and they can found or capture as many cities as they want.

Seems like it'd kinda suck to not get any sort of pillage reward, but ok.