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AM Radio has an extremely important role in emergency broadcasting, because you can cover a whole continent using just 3-4 broadcasting stations, and it is so easy to demodulate, that you can build completely analog recievers that need no power source (they use the carrier wave as a power source). This also means that AM receivers are very cheap, so in a lot of developing countries the only broadcasts most people can afford, and will reach them are AM.
I think we should keep AM radio around, at least for emergencies.
Also, unfortunately, when HF bandwidth gets freed up, it mostly ends up going to companies that use it for high frequency trading, and not to things where it would benefit the public, like ham radio, or digital broadcasts.
They do, but compounding errors are always a problem with inertial navigation.
Instead of GPS, they can use fixed radio beacons like VOR and TACAN (which I think are both just US systems, but there are similar systems around the world and at major airports). This is basically the system that was in use before GPS.
EDIT: grammar