The iron core but there are many open questions https://news.mit.edu/2020/origins-earth-magnetic-field-myste...

In case of Earth, Wikipedia describes [1] it as being "[..] generated by electric currents due to the motion of convection currents of a mixture of molten iron and nickel in Earth's outer core". This makes Earth a geodynamo [2]. (The aforementioned Wikipedia page is actually really long and detailed, a lot more than I would have thought)

[1] https://en.wikipedia.org/wiki/Earth%27s_magnetic_field [2] https://en.wikipedia.org/wiki/Dynamo_theory

No, otherwise Mars would have a magnetic field just like Earth.

Basically: moving electric charge = magnetic field. It's equivalent, that's why it's called electromagnetism: it's one and the same force.

The Earth rotates, liquid iron (inside Earth) flows => a current flows in the iron => there is a magnetic field.