The moving map could easily be fed from a separated consumer grade GPS. Same for all other metrics that the median passenger would care about (height, speed over ground), except for the ever-impressive outside temperature.
Most/all international flights I've been on are really terrible at providing an accurate flight plan or ETA to the passengers via the entertainment system. I would not be surprised if it is already a manual update done when convenient by a member of the flight crew.
They tend to use what's programmed in the FMS. Pilots will have the cleared route in there, even if they already know that they'll probably get several short cuts along the way.
I have never seen one that showed a flight plan. They only had a straight-line (well, a great circle route) to the destination. ETA was pretty clearly straight-line distance divided by (average?) speed.
Consumer grade GPS actually won't work at 30,000+ feet at speeds the plane would be flying. This is to prevent someone from using the GPS system to steer a ballistic missile.
My cell phone GPS works at cruise on an airplane. I can't attest to how location accurate it is but the altitude and speed are usually right on with what the infotainment system says.
The gps on my phone begs to differ. You can (sometimes) acquire enough gps locks to get a signal and subsequent gps data like speed, position, etc. Worth a shot trying because there's very few other times where you'd be able to see your gps sensor read 600mph. You're probably right though, it's just that the cutoff speed is higher than whatever a commercial jetliner speed is.