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I’m with you on point 1, (I think this is also obvious from experiment because you will never measure a particle at both slits).

for point 2 it seems you can define a mapping from the physical space to probability space. Saying that the wave doesn’t “move through” space might be technically correct but also seems like semantics on the definition of the phrase “move through” ?

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Of course it is to some extent semantics. But the important point is that the wavefunction is not something like a sound wave, or even something like a classical EM wave. Those are all waves defined over 3-dimensional physical space.

In the original QM model, light is not a wave in the classical electrical theory sense. Light is made up entirely of photons, which are particles just like electrons or billiard balls, and they are described by a wavefunction. That wavefunction gives them various probabilities of being in various states at a certain time, and those probabilities can increase or decrease when more particles come into the mix. The states can represent position, momentum, charge, spin, energy levels, etc.

Interference pattern is a measurement of a particle at both slits.

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