High-end dual-frequency receivers ($$$) can do this, yes. But the earth's magnetic field is not controlled by any government or military entities. This is pretty big

Yes and no. They often use GPS assisted by beacons. Those beacons are often set up using both high quality GPS but also surveying tools, and you might have seen markers in the ground on cities which was placed using very well calibrated tools so it has a well known very precise precision. Those beacons are easier to track for other machinery because they are so much closer so the radio signal is much clearer and angular precision is much better

I've played with GPS from several different directions. There are a lot of GPS receivers on the hobby electronics market that will offer that level of precision, but not accurately. The aviation wide area augmentation system significantly increases accuracy to the point it can be used for precision instrument approaches.

Not a single gps but multiple, the same trick could be done with this theoretically