Interesting questions! I hope I can shed some sunlight on them.
As stated in the abstract that you quote, understanding and modeling of sunspots is an open question, especially the question how the stability of sunspots is sustained.
There are many models, as your citations indicate. First, some terminological clarification: the "<PERSON> effect" nowadays is essentially a model to explain the physics of the sunspot. The "<PERSON> depression" is an observable component of a sunspot: the geometric height of the visible solar surface is depressed compared to the rest of the Sun. AT the time of <PERSON>, it was a hypothesis, but such depressions have been measured, e.g., see the figure here. In principle, since the idea is that the sunspot is generated by convective activity below the photosphere (i.e., convective heat transport is blocked by intense magnetic fields, which is why strong magnetic fields are needed to sustain a stable sunspot), the sunspot could be much deeper than what we're able to observe, since we cannot see directly below the photosphere (since the Sun's plasma becomes too opaque).
There are other models to explain the depression of a sunspot. For example, a recent model, which is (apparently) free from any systematic uncertainties due to no model-dependent assumptions, minimizes the divergence of the magnetic field derived from spectropolarimetric observations. By applying their framework to observations of a sunspot, they state:
The derived <PERSON> depression (∼600 km) is consistent with results typically obtained from the <PERSON> effect.
Their results are consistent with those of studies that employ the <PERSON> effect, e.g., as you cite from the 2009 Saas Fee Advanced Course 39.
So, your questions:
I would appreciate if somebody could explain [to] me the rather large range of depths. On the one hand, I am interested in the depth of the umbra measured from the penumbra (if it can be seen as flat), and on the other hand I also would like to know the distance from the penumbra to the end of the (visible) photosphere, everything ideally with errorbars.
To produce a plot with more precise answers and with errorbars would involve somebody already made such a plot, or I would have to make one. I do not have the time to do so myself, and I cannot find a published paper with it (it could be out there). So, I'll try to explain more conceptually. 70
Also, we cannot see below the photosphere so I think indirect methods would have to be used to obtain errorbars on observations of the depth of the umbra, which I am having trouble finding (and doubting if it's been done yet! EDIT: see the very last para. about helioseismology).
The wiki article states: "The magnitude of the depression is difficult to determine, but may be as large as 1,000 km." But it does not cite this claim ;)
Models of the <PERSON> effect, like those that you cite, are attempting to explain the emergence of a sunspot as originating from within the convective envelope of the stellar interior. Is that reasonable?: the depth cited of $\sim 7.3$Mm for these swells of plasma are at least within the solar radius, which is $\sim 10^9$m = 1 Gm. The photosphere is the deepest into the sun's interior that we can see optically, and it extends to about 4x10$^5$m. So it is conceivable that the sunspot can exist at depths below the photosphere inside a convective region of the sun without the bottom of the sunspot being too deep.
ADDED EDIT: In the models of <PERSON> and <PERSON>, e.g., 2014, "sunspot stability [is] a function of their radius and magnetic field strength [which] varies monotonically with radius from about 700 G up to an asymptotic limit of about 4000 G. The depth of the Wilson depression grows linearly with B. The range of stable equilibria is limited in a way that larger sunspots (radius larger than about 12–18 Mm) are unstable, which may explain the absence of very large sunspot on the Sun, as well as the appearance of the light bridges in large sunspots dividing them in several parts. Sunspots with B in the range of 2.6–2.7 kG and an umbral radius of about 2 Mm are the most stable." Quote taken from Note 4. of this helioseismology review (also in last para. below), and see Figure 22 of that review for a schematic of their model. 70