You cannot violate Earnshaw's theorem with static magnets. For the possible loopholes, see en.wikipedia.org/wiki/Earnshaw%27s_theorem#Loopholes

The electron would have to be in a bound system, such as an atom or a molecule, in order to have energy levels. Free electrons can only have momentum and intrinsic properties.

but in my answer I chose to stay away from the concepts of phase and group velocity, because they are not required to answer the original question as asked. As an experimental laser physicist, I prefer to give answers that can be explained with simple experiments.

Group velocity greater than c occurs under some conditions; see en.wikipedia.org/wiki/….

the phase velocity can be greater than c, but information never travels faster than c.

It's actually because natural polarizers, such as certain crystals, and reflections at Brewster's angle, work on the electric field. So it is more than a convention, it is the natural way to formulate it in terms of experimental effects. Note that the measurement of polarization pre-dates electromagnetic field theory.

s and p always refer to the plane of incidence; H and V usually refer to the orientation of the laser wrt the optical table surface.

You would need to study the line profiles to see if the broadening is due to a series of close lines, or if it is dominated by Doppler shifts. The statistics are quire clear, and you will study this in a quantum optics class.

If you want a low divergence beam, you must use two lenses, and construct a telescope (beam expander), e.g., edmundoptics.com/resources/application-notes/optics/…

Look for information on the magnetosphere.

To explain the question from your title: electronics-tutorials.ws/accircuits/rms-voltage.html