Appears the guests may have left the faucet "on" when the pipes were frozen and when no water came out, forgot to turn it "off".What may have caused the overflow of the sink is maybe the drain lines were also frozen?

Then wherever the water is getting discharged off of the roof, that what water is getting at least 4-5 foot away from the structure before it is left to drain with gravity away from the property. 

Water meter-water company.  

Water overflowing the sink, seems more plausible than some missing caulk.  

What if you turn on water and it goes everywhere.

And I will state different jurisdictions have different rules, processes, expectations, etc.In my area you are required to have a permit to swap a water heater.

Quote from @Aaron Wolman: I would call the companies (gas/water/electric) to get estimates, or an estimator out there.

City water with one main at the street and how will they bill. 

The meters are read electronically with 3g and you get great reporting in their water scope platform.

I used to live in the city and the taxes and water bills are nightmares.