[Jarek Duda (OP)]

While electron and proton being far apart are allowed to be imagined as nearly point particles, when they approach ~10^-10m (or much more for Rydberg atoms), electron is said "to become" this relatively huge wavefunction - orbital, describing probability distribution of finding electron (confirmed experimentally e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 ).

Can we specify in what e-p distance this qualitative change happens?

How to think about this orbital from QM interpretations perspective - is it superposition of electron (indivisible charge) being in all these places? Is electric field of orbital a superposition over electron being in all places, or rather mean?

E.g. in Many Worlds Interpretation, should we imagine that electron has different position in each World?

In such superposition each electron is staying or moving? If staying, where e.g. the orbital angular momentum comes from? If moving, why no synchrotron radiation?

[evan_au]

Can we specify in what e-p distance this qualitative change happens?

I don't think that there is a qualitative change - an electron has some properties of both a particle and wave at the same time.

What matters is how you measure the electron - some measurement methods emphasize one aspect more than the other.
- But until you measure the position of an electron, it could be anywhere (with a certain distribution of probabilities)
- After you measure it once, the distribution of probabilities will be different

As soon as an electron falls within the electric field of a proton, most methods to detect electrons will be impacted by the presence of a positive proton in the vicinity.
- and electric fields extend "to infinity"

[Jarek Duda (OP)]

Remember that electron is charged - hence has accompanied electric field.

So what is electric field of orbital?
Is it superposition of electric field of electron being in each point?
Or maybe it is one electric field averaged over electron position?

I don't think that there is a qualitative change

Indeed we are entering the complementary principle ( https://en.wikipedia.org/wiki/Complementarity_(physics) ) allowing to measure only one at once.
But measurement is very destructive process, the question is if they are objectively both?
One experiment using both is Afshar's: https://en.wikipedia.org/wiki/Afshar_experiment
A more recent one "Simultaneous observation of the quantization and the interference pattern": https://www.nature.com/articles/ncomms7407
For atom-like models with orbital quantization, there are great walking droplets experiments e.g. https://www.nature.com/articles/ncomms4219 or www.pnas.org/content/107/41/17515.short

[Jarek Duda (OP)]

Ps. Just found 2008 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.073003 "Scientists in Sweden film moving electron for the first time":

They see wave nature, but clearly localized - with traveling center, exactly as in walking droplets experiments https://dualwalkers.com/