some cars the power port stays on key off, some turn off when the key is off, has nothing to do where its made or sold.
get the battery load tested too. as well as the alts volts.
you battery is likely dead, i also lost the battery in my tahoe 2 weeks ago. failed to even take a charge, or jump start. best i got was a slow crank and click click click.....
always unplug your power ports when its this cold. the extra drain will help kill it over night.
that fan turning on is also a issue, ignition harness gone bad could cause this, or maybe the fan resistor is going bad, some how its getting power with out being told so. you could pull its fuse and see if the batterys dead in the morning to.
