Where does the water go afterwards? Is it evaporated? Sewer?

I believe evaporative cooling is the norm (thus my "possibly many times that" remark doesn't apply) however theoretically they could provide hot water as a utility or (as you say) just dump it into the sewer. If located next to a river or the ocean they could conceivably dissipate it that way but I'm not aware of any examples.

It's the sort of externality that could be solved with a well placed megaproject. A related question to my mind is why we're building such expensive strategic assets in the open rather than under a mountain.

Evaporated. Given how the water cycle works, it should be expected it will be precipitated back as rain.