Hello,

This is not a contradiction, because a priori is different data than a posteriori.

Yes, and that's why the position/parameter is improved by further observations. If both are identical, the parameter is fixed.

The point can remain fixed with additional stochastic information; e.g. think about the stochastic model of a mark or of a bolt.

Marking a point is a simple realization of a random experiment but with a single draw. The marked position is not the true value, i.e., if you repeat the marking procedure several times you will not end up with identical positions. These deviations are characterized by the stochastic model and the position is improved by further information e.g. observations in least-squares. It is simple application of statistic. You shouldn't draw conclusions from a single draw - that's a fallacy.

In theory, the point is fixed

Theoretically, there is a true position of the point that has certain coordinates. The true value is inherently not associated with any uncertainty. However, as long as you do not know the true position, you have to deal with uncertainties and imperfections.

I didn't try it, but maybe one could artificially introduce "observations of direction 0 gon, vertical zenith angle 0 gon, and distance 0m"

It is easy to verify that this procedure fails. Just take a look at the partial derivations.

Kind regards
Micha