About "leakage inductance"

Apparently, there is only one "leakage inductance" at one side in the figure above.

No, that is incorrect.

Every winding in a transformer does not couple 100% to each other winding and that is a fact. If some piece of text suggests that the leakage inductance is only attributable to one winding then that piece of text is at best misleading and, at worst blatantly wrong.

However, from the perspective of someone wishing to know how well two windings may couple then a single entity of leakage (a composite of both leakages) can be used to express that.

As for your 2nd question, you CANNOT short the secondary at the point you wish. This IS impossible - you can't take the equivalent circuit of the transformer and hack at it like that. The leakage measured is the composite leakage and this can be broken down into two components by using the turns ratio squared but even that is only an approximation; the magnetization inductance will alter the accuracy of this method slightly but, for all practical purposes, this method yields fairly accurate results.

First, imagine a core with one winding of N turns. If the winding carries has a voltage V across it, then the flux linked to it Must change at a rate V/N. Now, most (99%) of this flux increase happens through the core, but the rest circulates through the air. The flux (rate) through the air is the leakage component and can be modelled as a bulk leakage inductance.

Now on this core lets wind another coil, again with N turns. The core already has a flux caused by coil 1. Most of this flux passes though the second coil, generating an emf, but some of it "bypasses" this coil and passes through the air instead. This is modelled as the secondary leakage inductance. To simplify the circuit model it is possible to combine both inductances into one "lumped" inductor.

One can measure the leakage inductance on the primary or on the secondary. Both results reflect the total leakage adjusted by the turns ratio and summed up. That is all ok. Problems will show up if the parasitic capacitance of the winding at high frequencies become more dominant. Then you need to split the leakage inductance correctly to each side with its own parasitic components to get a useful model to reflect for example self resonances of the transformer correctly. Otherwise even the VOLTEC model will work for most applications.