electromagnetism - Electrons and Magnetism

Electron at rest generates Electric field. Electron moving without acceleration produces electric and magnetic field. Electron moving with acceleration produces electromagnetic waves.

Please explain the mechanism or the process how this happens. How magnetic field is generated by moving charges? (A moving charge produces a current, or rather a time varying electric field in space.)

Also link https://www.physicsforums.com/threads/why-does-moving-electron-produce-magnetic-field.184619/ said

A moving electron alone actually does not produce a magnetic field. It requires electrons and protons to produce a magnetic field. As the electrons move relative to protons (ions) there is a relativistic charge per unit volume difference between the positive and the negative charges. This causes any external charges to feel a force we know as the magnetic field.

The magnetic field is a relativistic correction to the electrostatic field.

I could not understand these lines. And I don't know much about quantum physics. So, can you please explain in a simpler way? Please use quantum physics also, if it works here.. I may understand it sooner or later.

Also how electromagnetic waves are produced by accelerating charges? An electron with more energy gives it out in the form of photons i.e., E.M. waves. Is it that electric and magnetic fields produced by electron superpose? That could not have possibly happened because varying electric and magnetic field give rise to each other independently..

What happens there actually? And how magnetic field is relativistic correction to electric field?

Thank you.