Had a bad Ford alternator which did this. Recharge the battery, re-connect the cables and see if you feel the alternator heating up. Could be an internal short. Another option is charge the battery and unplug the alternator to see if the battery still dies over night.
Have you tried to pull each fuse and use a light across the terminals the fuses plug into to find out what is drawing current when the car is off? Do the same with plug in circuit breakers if you find any.
I believe you will find a fuse block inside the car as well as under the hood on left inner fender.
You may also want to put the new battery on a tester to verify it is not defective.
Try unplugging the fan control box (power train control module) mountdr next to your radiator overflow tank and see if the battery goes dead overnight. They are known to have problems and could have shorted inside. The high current from the fan causes the relay and other components to burn up inside. Is probably reason you cooling engine fan does not work.
https://www.rockauto.com/en/moreinfo.php?pk=944041&cc=1134188&jsn=501
The engine fan is turned on by the engine computer temperature sensor. It closes a relay in the above box which puts power to the fan. The gauge temperature sensor is a separate sensor which I believe is mounted towards the drivers side rear of the intake manifold. If your engine computer temperature sensor was bad, the engine would not run (or run very poor)
Look up the temperature sensors on Rockauto under the cooling section. The gauge sensor is shown with a threaded stud on the top which the wire connects to. The engine coolant sensor has a plastic plug connector on the top of it.