This is a cool topic to imagine...
As it was sort of foreseen in #7: The Stranger and also in #41: The Familiar, we know what to expect of Earth under Yeerk domination.
It would have very much been mostly human-Controllers going about the surface on high-tech transport, without any unessential contact, purposefully going about their organized tasks to the Yeerk Empire. Maybe their equivalent of 'Sundays' would have been some vacations on the open ground-based pools, as opposed to their military service complexes.
The human race would have ended as we knew it. All human-made stuff that isn't valuable to the Yeerks, such as ornaments, landmarks, entertainment, surpassed-technology (the wheel, guns, tv, cars, computers, etc), historical records, etc... would have been destroyed. Human governments would be c-o-m-p-l-e-t-e history!
Whatever product of the human race they didn't want to incorporate, they would incenarate.
They may well chose to adopt the name of our nations as a form of separating zones of their new territory. And if so, even make use of some constructed suburbias.
But I cannot actually imagine (as some might picture) Yeerks spread throughout the 7 continents, living in mass civilized settlements (converted cities), serenely adapting to their human-Controllers way of life and mimicking the host's somewhat past daily routines. While being Controllers on Earth, they would STILL have some Sub-Visser or Visser or Council of Thirteen to submit to.
The Yeerks would have depleted Earth of all of its mineral resources. There would have been talks about drying out the oceans for more land.
I am not sure now if they WOULD have terminated all unecessary animals, since with the newly acquired Morphing tech they HAD to preserve animal species for 'ammunition' (to call it that). Not executing animals would mean, preserving animal habitats... So there's their whole 'destruction of Earth' execution hindered. But I still think, with the surface of the Earth changed, its atmosphere would follow.
... i mean to start, I can see human puppet governments being set up, like what the Nazis did in Vichy France.
PS:
Azguard, call me ignorant, but I don't really know what the Nazis did here...