It's not a magnet that's moving. It's electric charge that's moving, which is how magnetic fields are generated.

It's fine to say we don't know for sure what's down there. It is based on inference from indirect sources, but the model of what's down there is fairly detailed and does account for the major phenomena we do observe directly.

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The iron wouldn't maintain a magnetic charge at those temperatures.

You've got it the wrong way around; electric fields are created by moving magnetic fields.

I don't know where you're getting any of this, but moving electrical charge (aka current) does create a magnetic field. Consult literally any textbook on electricity and magnetism.

Here's one source amongst many: https://www.studypug.com/physics-help/electric-currents-produce-magnetic-fields