3 - The fact that you have consistent results (your noted 2 mpg variance between manual calculation and computer) says something about the process used.
If there were inaccuracies introduced by the pump, you would not get a consistent calculation compared to the computer - These would vary... but they didn't.
I'm thinking there is a good reason for a 2 mpg variance being reported by the software - The user believes they are getting better mpg... and if they never check with a manual calculation, there is no reason for them to believe otherwise, but that doesn't mean the number is right.
One of the tenents of evaluation of a process is a confirmation of the measurement system.
Your results proved that there was a difference between the two measurements, and the consistent difference proves that both measurements are repeatable, but what hasn't been proved is if either one or both is accurate.
While it is impossible to evaluate the components of the automated system without access to source software and test results of the individual components providing data to that process, it is relatively simple to ascertain the manual calculation components, as these can be independently verified.
Mileage by following a known distance and volume of fuel using a measured container. The calculation itself is immune from variation.
Many roads have speedometer/odometer checks, so it the car's odometer is correct when compared to the mileage on a known course, the only variable is the fuel volume. A couple of translucent marked volume cans could easily provide that.
Myself, it's not worth the effort to do the experiment. I know my odometer is correct, and I've added fuel just after weights and measures verified a local pump.
My car's computer says I get 2 mpg more than what I measure, and that has been as consistent as your results.
It therefore appears that the computer is incorrect, and perhaps intentionally so, as there is a good reason for the system developer to skew the results to the positive. There is no law stating that the car's internal data reporting system is accurate.