By “tend to push back if they get too close” do you mean just regular electrostatic repulsion between like charges, or are you referring to the phenomenon of electron degeneracy pressure? Because the latter is far more interesting. It’s another bit of quantum weirdness resulting from the exclusion principle where two identical electrons will refuse to occupy the same quantum state (same “orbit”) as each other. Keeps white dwarf stars from collapsing into neutron stars and has nothing to do with the regular repellence that identical charges experience.

As for spin, that’s again another very strange property of quantum particles. The spin of an atom is fairly easily explained by the sum of spins of its components (plus a bit from orbital angular momentum) but that just begs the question what it means for an electron to have “spin”? A point charge cannot technically rotate, nevertheless electrons clearly have an intrinsic magnetic dipole moment and this is what we call spin. But the way it behaves is far more interesting than what you would imagine when you picture a macroscopic analog like a planet spinning.

For instance electron spin is fractional and discrete. Its orientation is also changed by measurement in a very similar way to how the polarization of light waves works (because photons also have spin). A downright bizarre consequence of the fractional spin of particles like electrons is that they do not behave under rotation like normal objects do. When you rotate anything in the macroscopic world 360° you end up right where you started. Not so for the wave function of an electron. If you want to “rotate” that “all the way around”, you need to go 720°.

Anyway, just some tidbits i find interesting about this subject.