There are few issues at play here. 1 is the actual value that the sender is putting out, 2 is the averaged value that the ECU is interpreting it to, and 3 is the dumbed down version that it decides to show you.
You can't see the value for 1 unless you intercept the voltage from the sender unit, but you can watch the value for 2 using an OBDII reader. The value changes significantly depending on how you are driving, and will creep up while you are stationary. The value for 3 seems to never go up unless you turn off the car, in which case it will reset to the value it gets from step 2.
As far as running out of fuel goes, you can drive down to the last drop if you drive like an old lady and avoid hills, but due to the tank design you in reality need a buffer of at least 3 gallons for average driving and 10 gallons for aggressive driving. The car seems to be calibrated so that it will read empty (no lights, 0 mile range) when you have approximately 2-3 gallons left in the tank.
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